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University of Michigan

1. Yin, Qian. Lattes Maps and Combinatorial Expansion.

Degree: PhD, Mathematics, 2011, University of Michigan

URL: http://hdl.handle.net/2027.42/86524

► A Lattes map f : C → C is a rational map that is obtained from a finite quotient of a conformal torus endomorphism. In…
(more)

Subjects/Keywords: Lattes Maps; Thurston Maps; Sphere; Postcritically Finite; Mathematics; Science

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APA (6^{th} Edition):

Yin, Q. (2011). Lattes Maps and Combinatorial Expansion. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/86524

Chicago Manual of Style (16^{th} Edition):

Yin, Qian. “Lattes Maps and Combinatorial Expansion.” 2011. Doctoral Dissertation, University of Michigan. Accessed August 07, 2020. http://hdl.handle.net/2027.42/86524.

MLA Handbook (7^{th} Edition):

Yin, Qian. “Lattes Maps and Combinatorial Expansion.” 2011. Web. 07 Aug 2020.

Vancouver:

Yin Q. Lattes Maps and Combinatorial Expansion. [Internet] [Doctoral dissertation]. University of Michigan; 2011. [cited 2020 Aug 07]. Available from: http://hdl.handle.net/2027.42/86524.

Council of Science Editors:

Yin Q. Lattes Maps and Combinatorial Expansion. [Doctoral Dissertation]. University of Michigan; 2011. Available from: http://hdl.handle.net/2027.42/86524

University of Michigan

2. Parra Casta, Manuel Rodrigo. Currents and Equidistribution in Holomorphic Dynamics.

Degree: PhD, Mathematics, 2011, University of Michigan

URL: http://hdl.handle.net/2027.42/89619

► Given a holomorphic self-map of complex projective space of degree larger than one, we prove that there exists a finite collection of totally invariant algebraic…
(more)

Subjects/Keywords: Dynamical Systems; Equidistributiom; Ergodic Theory; Green Current; Mathematics; Science

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APA (6^{th} Edition):

Parra Casta, M. R. (2011). Currents and Equidistribution in Holomorphic Dynamics. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/89619

Chicago Manual of Style (16^{th} Edition):

Parra Casta, Manuel Rodrigo. “Currents and Equidistribution in Holomorphic Dynamics.” 2011. Doctoral Dissertation, University of Michigan. Accessed August 07, 2020. http://hdl.handle.net/2027.42/89619.

MLA Handbook (7^{th} Edition):

Parra Casta, Manuel Rodrigo. “Currents and Equidistribution in Holomorphic Dynamics.” 2011. Web. 07 Aug 2020.

Vancouver:

Parra Casta MR. Currents and Equidistribution in Holomorphic Dynamics. [Internet] [Doctoral dissertation]. University of Michigan; 2011. [cited 2020 Aug 07]. Available from: http://hdl.handle.net/2027.42/89619.

Council of Science Editors:

Parra Casta MR. Currents and Equidistribution in Holomorphic Dynamics. [Doctoral Dissertation]. University of Michigan; 2011. Available from: http://hdl.handle.net/2027.42/89619

University of Michigan

3. Weiss, Benjamin Leonard. Diophantine Equations With Two Separated Variables.

Degree: PhD, Mathematics, 2011, University of Michigan

URL: http://hdl.handle.net/2027.42/89707

► We classify pairs of polynomials G, H ∈ C[T ] such that G(X ) = H (Y ) defines an irreducible curve of genus zero,…
(more)

Subjects/Keywords: Diophantine Equations; Polynomial Decomposition; Genus of Curve; Mathematics; Science

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APA (6^{th} Edition):

Weiss, B. L. (2011). Diophantine Equations With Two Separated Variables. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/89707

Chicago Manual of Style (16^{th} Edition):

Weiss, Benjamin Leonard. “Diophantine Equations With Two Separated Variables.” 2011. Doctoral Dissertation, University of Michigan. Accessed August 07, 2020. http://hdl.handle.net/2027.42/89707.

MLA Handbook (7^{th} Edition):

Weiss, Benjamin Leonard. “Diophantine Equations With Two Separated Variables.” 2011. Web. 07 Aug 2020.

Vancouver:

Weiss BL. Diophantine Equations With Two Separated Variables. [Internet] [Doctoral dissertation]. University of Michigan; 2011. [cited 2020 Aug 07]. Available from: http://hdl.handle.net/2027.42/89707.

Council of Science Editors:

Weiss BL. Diophantine Equations With Two Separated Variables. [Doctoral Dissertation]. University of Michigan; 2011. Available from: http://hdl.handle.net/2027.42/89707

University of Michigan

4. Wyman, Brian Kenneth. Polynomial Decomposition Over Rings.

Degree: PhD, Mathematics, 2010, University of Michigan

URL: http://hdl.handle.net/2027.42/77772

► We study of the arithmetic of polynomials under the operation of functional composition, namely, the operation of functional compositon: f(x) ∘ g(x) := f(g(x)). This…
(more)

Subjects/Keywords: Polynomial Decomposition; Number Theory; Algebra; Ring Theory; Polynomial; Mathematics; Science

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APA (6^{th} Edition):

Wyman, B. K. (2010). Polynomial Decomposition Over Rings. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/77772

Chicago Manual of Style (16^{th} Edition):

Wyman, Brian Kenneth. “Polynomial Decomposition Over Rings.” 2010. Doctoral Dissertation, University of Michigan. Accessed August 07, 2020. http://hdl.handle.net/2027.42/77772.

MLA Handbook (7^{th} Edition):

Wyman, Brian Kenneth. “Polynomial Decomposition Over Rings.” 2010. Web. 07 Aug 2020.

Vancouver:

Wyman BK. Polynomial Decomposition Over Rings. [Internet] [Doctoral dissertation]. University of Michigan; 2010. [cited 2020 Aug 07]. Available from: http://hdl.handle.net/2027.42/77772.

Council of Science Editors:

Wyman BK. Polynomial Decomposition Over Rings. [Doctoral Dissertation]. University of Michigan; 2010. Available from: http://hdl.handle.net/2027.42/77772

5. Hyde, Trevor. Polynomial Statistics, Necklace Polynomials, and the Arithmetic Dynamical Mordell-Lang Conjecture.

Degree: PhD, Mathematics, 2019, University of Michigan

URL: http://hdl.handle.net/2027.42/151684

► This thesis consists of six chapters representing two directions of the author’s graduate research under the advisement of Jeffrey Lagarias and *Michael* *Zieve*. The first…
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Subjects/Keywords: Configuration space; Necklace polynomial; Dynamical Mordell-Lang; Mathematics; Science

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APA (6^{th} Edition):

Hyde, T. (2019). Polynomial Statistics, Necklace Polynomials, and the Arithmetic Dynamical Mordell-Lang Conjecture. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/151684

Chicago Manual of Style (16^{th} Edition):

Hyde, Trevor. “Polynomial Statistics, Necklace Polynomials, and the Arithmetic Dynamical Mordell-Lang Conjecture.” 2019. Doctoral Dissertation, University of Michigan. Accessed August 07, 2020. http://hdl.handle.net/2027.42/151684.

MLA Handbook (7^{th} Edition):

Hyde, Trevor. “Polynomial Statistics, Necklace Polynomials, and the Arithmetic Dynamical Mordell-Lang Conjecture.” 2019. Web. 07 Aug 2020.

Vancouver:

Hyde T. Polynomial Statistics, Necklace Polynomials, and the Arithmetic Dynamical Mordell-Lang Conjecture. [Internet] [Doctoral dissertation]. University of Michigan; 2019. [cited 2020 Aug 07]. Available from: http://hdl.handle.net/2027.42/151684.

Council of Science Editors:

Hyde T. Polynomial Statistics, Necklace Polynomials, and the Arithmetic Dynamical Mordell-Lang Conjecture. [Doctoral Dissertation]. University of Michigan; 2019. Available from: http://hdl.handle.net/2027.42/151684

6. Kopp, Gene. Indefinite Theta Functions and Zeta Functions.

Degree: PhD, Mathematics, 2017, University of Michigan

URL: http://hdl.handle.net/2027.42/140957

► We define an indefinite theta function in dimension g and index 1 whose modular parameter transforms by a symplectic group, generalizing a construction of Sander…
(more)

Subjects/Keywords: number theory; indefinite theta function; zeta function; real quadratic field; Kronecker limit formula; SIC-POVM; Mathematics; Science

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Kopp, G. (2017). Indefinite Theta Functions and Zeta Functions. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/140957

Chicago Manual of Style (16^{th} Edition):

Kopp, Gene. “Indefinite Theta Functions and Zeta Functions.” 2017. Doctoral Dissertation, University of Michigan. Accessed August 07, 2020. http://hdl.handle.net/2027.42/140957.

MLA Handbook (7^{th} Edition):

Kopp, Gene. “Indefinite Theta Functions and Zeta Functions.” 2017. Web. 07 Aug 2020.

Vancouver:

Kopp G. Indefinite Theta Functions and Zeta Functions. [Internet] [Doctoral dissertation]. University of Michigan; 2017. [cited 2020 Aug 07]. Available from: http://hdl.handle.net/2027.42/140957.

Council of Science Editors:

Kopp G. Indefinite Theta Functions and Zeta Functions. [Doctoral Dissertation]. University of Michigan; 2017. Available from: http://hdl.handle.net/2027.42/140957

7. Scherr, Zachary L. Rational Polynomial Pell Equations.

Degree: PhD, Mathematics, 2013, University of Michigan

URL: http://hdl.handle.net/2027.42/100026

► Let R denote either the integers or the rationals and let d(x) be a square-free polynomial in R[x]. In this thesis we study the question…
(more)

Subjects/Keywords: Number Theory; Polynomial Pell Equations; Mathematics; Science

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APA (6^{th} Edition):

Scherr, Z. L. (2013). Rational Polynomial Pell Equations. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/100026

Chicago Manual of Style (16^{th} Edition):

Scherr, Zachary L. “Rational Polynomial Pell Equations.” 2013. Doctoral Dissertation, University of Michigan. Accessed August 07, 2020. http://hdl.handle.net/2027.42/100026.

MLA Handbook (7^{th} Edition):

Scherr, Zachary L. “Rational Polynomial Pell Equations.” 2013. Web. 07 Aug 2020.

Vancouver:

Scherr ZL. Rational Polynomial Pell Equations. [Internet] [Doctoral dissertation]. University of Michigan; 2013. [cited 2020 Aug 07]. Available from: http://hdl.handle.net/2027.42/100026.

Council of Science Editors:

Scherr ZL. Rational Polynomial Pell Equations. [Doctoral Dissertation]. University of Michigan; 2013. Available from: http://hdl.handle.net/2027.42/100026

8. Mueller, Alexander. Applications of Generalized Fermat Varieties to Zeta Functions of Artin-Schreier Curves.

Degree: PhD, Mathematics, 2013, University of Michigan

URL: http://hdl.handle.net/2027.42/99918

► We outline an approach to studying Artin-Schreier curves X_{f} (associated with equations of the form y^{q-y}=f(x)) involving auxiliary varieties of higher dimension. Specifically, for a…
(more)

Subjects/Keywords: Number Theory; Algebraic Geometry; Exponential Sums; Artin-Schreier Curve; Mathematics; Science

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APA (6^{th} Edition):

Mueller, A. (2013). Applications of Generalized Fermat Varieties to Zeta Functions of Artin-Schreier Curves. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/99918

Chicago Manual of Style (16^{th} Edition):

Mueller, Alexander. “Applications of Generalized Fermat Varieties to Zeta Functions of Artin-Schreier Curves.” 2013. Doctoral Dissertation, University of Michigan. Accessed August 07, 2020. http://hdl.handle.net/2027.42/99918.

MLA Handbook (7^{th} Edition):

Mueller, Alexander. “Applications of Generalized Fermat Varieties to Zeta Functions of Artin-Schreier Curves.” 2013. Web. 07 Aug 2020.

Vancouver:

Mueller A. Applications of Generalized Fermat Varieties to Zeta Functions of Artin-Schreier Curves. [Internet] [Doctoral dissertation]. University of Michigan; 2013. [cited 2020 Aug 07]. Available from: http://hdl.handle.net/2027.42/99918.

Council of Science Editors:

Mueller A. Applications of Generalized Fermat Varieties to Zeta Functions of Artin-Schreier Curves. [Doctoral Dissertation]. University of Michigan; 2013. Available from: http://hdl.handle.net/2027.42/99918

9. Rosen, Julian H. The Arithmetic of Multiple Harmonic Sums.

Degree: PhD, Mathematics, 2013, University of Michigan

URL: http://hdl.handle.net/2027.42/99893

► This dissertation concerns the arithmetic of a family of rational numbers called multiple harmonic sums. These sums are finite truncations of multiple zeta values. We…
(more)

Subjects/Keywords: Multiple Harmonic Sums; Mathematics; Science

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APA (6^{th} Edition):

Rosen, J. H. (2013). The Arithmetic of Multiple Harmonic Sums. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/99893

Chicago Manual of Style (16^{th} Edition):

Rosen, Julian H. “The Arithmetic of Multiple Harmonic Sums.” 2013. Doctoral Dissertation, University of Michigan. Accessed August 07, 2020. http://hdl.handle.net/2027.42/99893.

MLA Handbook (7^{th} Edition):

Rosen, Julian H. “The Arithmetic of Multiple Harmonic Sums.” 2013. Web. 07 Aug 2020.

Vancouver:

Rosen JH. The Arithmetic of Multiple Harmonic Sums. [Internet] [Doctoral dissertation]. University of Michigan; 2013. [cited 2020 Aug 07]. Available from: http://hdl.handle.net/2027.42/99893.

Council of Science Editors:

Rosen JH. The Arithmetic of Multiple Harmonic Sums. [Doctoral Dissertation]. University of Michigan; 2013. Available from: http://hdl.handle.net/2027.42/99893

10. Gignac, William T. Equidistribution of Preimages in Nonarchimedean Dynamics.

Degree: PhD, Mathematics, 2013, University of Michigan

URL: http://hdl.handle.net/2027.42/99809

► One of the central results in holomorphic dynamics in several variables is the equidistribution of preimages theorem, which constructs invariant probability measures for a large…
(more)

Subjects/Keywords: Nonarchimedean Dynamics; Equidistribution of Preimages; Ergodic Theory; Holomorphic Dynamics; Good Reduction; Berkovich Analytic Spaces; Mathematics; Science

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Gignac, W. T. (2013). Equidistribution of Preimages in Nonarchimedean Dynamics. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/99809

Chicago Manual of Style (16^{th} Edition):

Gignac, William T. “Equidistribution of Preimages in Nonarchimedean Dynamics.” 2013. Doctoral Dissertation, University of Michigan. Accessed August 07, 2020. http://hdl.handle.net/2027.42/99809.

MLA Handbook (7^{th} Edition):

Gignac, William T. “Equidistribution of Preimages in Nonarchimedean Dynamics.” 2013. Web. 07 Aug 2020.

Vancouver:

Gignac WT. Equidistribution of Preimages in Nonarchimedean Dynamics. [Internet] [Doctoral dissertation]. University of Michigan; 2013. [cited 2020 Aug 07]. Available from: http://hdl.handle.net/2027.42/99809.

Council of Science Editors:

Gignac WT. Equidistribution of Preimages in Nonarchimedean Dynamics. [Doctoral Dissertation]. University of Michigan; 2013. Available from: http://hdl.handle.net/2027.42/99809

11. Simon, Gregory G. Automorphism-invariant Integral Forms in Griess Algebras.

Degree: PhD, Mathematics, 2016, University of Michigan

URL: http://hdl.handle.net/2027.42/133314

► Motivated by the existence of group-invariant integral forms in various vertex operator algebras, we classify maximal automorphism-invariant integral forms in some small-dimensional Griess algebras, which…
(more)

Subjects/Keywords: nonassociative algebras; integral forms; lattices; Mathematics; Science

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APA (6^{th} Edition):

Simon, G. G. (2016). Automorphism-invariant Integral Forms in Griess Algebras. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/133314

Chicago Manual of Style (16^{th} Edition):

Simon, Gregory G. “Automorphism-invariant Integral Forms in Griess Algebras.” 2016. Doctoral Dissertation, University of Michigan. Accessed August 07, 2020. http://hdl.handle.net/2027.42/133314.

MLA Handbook (7^{th} Edition):

Simon, Gregory G. “Automorphism-invariant Integral Forms in Griess Algebras.” 2016. Web. 07 Aug 2020.

Vancouver:

Simon GG. Automorphism-invariant Integral Forms in Griess Algebras. [Internet] [Doctoral dissertation]. University of Michigan; 2016. [cited 2020 Aug 07]. Available from: http://hdl.handle.net/2027.42/133314.

Council of Science Editors:

Simon GG. Automorphism-invariant Integral Forms in Griess Algebras. [Doctoral Dissertation]. University of Michigan; 2016. Available from: http://hdl.handle.net/2027.42/133314

12. Liu, Sijun. Functional Equations Involving Laurent Polynomials and Meromorphic Functions, with Applications to Dynamics and Diophantine Equations.

Degree: PhD, Mathematics, 2014, University of Michigan

URL: http://hdl.handle.net/2027.42/108867

► In this thesis, our main theorem gives the classification of all Laurent polynomials f(X) such that the numerator of frac{f(X)-f(Y)}{X-Y} has an irreducible factor whose…
(more)

Subjects/Keywords: Diophantine Equation; Functional Equation; Mathematics; Science

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APA (6^{th} Edition):

Liu, S. (2014). Functional Equations Involving Laurent Polynomials and Meromorphic Functions, with Applications to Dynamics and Diophantine Equations. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/108867

Chicago Manual of Style (16^{th} Edition):

Liu, Sijun. “Functional Equations Involving Laurent Polynomials and Meromorphic Functions, with Applications to Dynamics and Diophantine Equations.” 2014. Doctoral Dissertation, University of Michigan. Accessed August 07, 2020. http://hdl.handle.net/2027.42/108867.

MLA Handbook (7^{th} Edition):

Liu, Sijun. “Functional Equations Involving Laurent Polynomials and Meromorphic Functions, with Applications to Dynamics and Diophantine Equations.” 2014. Web. 07 Aug 2020.

Vancouver:

Liu S. Functional Equations Involving Laurent Polynomials and Meromorphic Functions, with Applications to Dynamics and Diophantine Equations. [Internet] [Doctoral dissertation]. University of Michigan; 2014. [cited 2020 Aug 07]. Available from: http://hdl.handle.net/2027.42/108867.

Council of Science Editors:

Liu S. Functional Equations Involving Laurent Polynomials and Meromorphic Functions, with Applications to Dynamics and Diophantine Equations. [Doctoral Dissertation]. University of Michigan; 2014. Available from: http://hdl.handle.net/2027.42/108867

13. Portilla, Ricardo. Finite Order Automorphisms and a Parametrization of Nilpotent Orbits in p-adic Lie Algebras.

Degree: PhD, Mathematics, 2011, University of Michigan

URL: http://hdl.handle.net/2027.42/86500

► Let k be a field with a nontrivial discrete valuation which is complete and has perfect residue field. Let G be the group of k-rational…
(more)

Subjects/Keywords: Group Theory; Bruhat-tits Theory; Mathematics; Science

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APA (6^{th} Edition):

Portilla, R. (2011). Finite Order Automorphisms and a Parametrization of Nilpotent Orbits in p-adic Lie Algebras. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/86500

Chicago Manual of Style (16^{th} Edition):

Portilla, Ricardo. “Finite Order Automorphisms and a Parametrization of Nilpotent Orbits in p-adic Lie Algebras.” 2011. Doctoral Dissertation, University of Michigan. Accessed August 07, 2020. http://hdl.handle.net/2027.42/86500.

MLA Handbook (7^{th} Edition):

Portilla, Ricardo. “Finite Order Automorphisms and a Parametrization of Nilpotent Orbits in p-adic Lie Algebras.” 2011. Web. 07 Aug 2020.

Vancouver:

Portilla R. Finite Order Automorphisms and a Parametrization of Nilpotent Orbits in p-adic Lie Algebras. [Internet] [Doctoral dissertation]. University of Michigan; 2011. [cited 2020 Aug 07]. Available from: http://hdl.handle.net/2027.42/86500.

Council of Science Editors:

Portilla R. Finite Order Automorphisms and a Parametrization of Nilpotent Orbits in p-adic Lie Algebras. [Doctoral Dissertation]. University of Michigan; 2011. Available from: http://hdl.handle.net/2027.42/86500

14. More, Ajinkya Ajay. Symbolic Powers and other Contractions of Ideals in Noetherian Rings.

Degree: PhD, Mathematics, 2012, University of Michigan

URL: http://hdl.handle.net/2027.42/94031

► The results in this thesis are motivated by the following four questions: 1. (Eisenbud-Mazur conjecture): Given a regular local ring (R,m) containing a field of…
(more)

Subjects/Keywords: Symbolic Powers, Eisenbud-Mazur Conjecture, Regular Local Ring, Uniform Bounds, Contractions; Mathematics; Science

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APA (6^{th} Edition):

More, A. A. (2012). Symbolic Powers and other Contractions of Ideals in Noetherian Rings. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/94031

Chicago Manual of Style (16^{th} Edition):

More, Ajinkya Ajay. “Symbolic Powers and other Contractions of Ideals in Noetherian Rings.” 2012. Doctoral Dissertation, University of Michigan. Accessed August 07, 2020. http://hdl.handle.net/2027.42/94031.

MLA Handbook (7^{th} Edition):

More, Ajinkya Ajay. “Symbolic Powers and other Contractions of Ideals in Noetherian Rings.” 2012. Web. 07 Aug 2020.

Vancouver:

More AA. Symbolic Powers and other Contractions of Ideals in Noetherian Rings. [Internet] [Doctoral dissertation]. University of Michigan; 2012. [cited 2020 Aug 07]. Available from: http://hdl.handle.net/2027.42/94031.

Council of Science Editors:

More AA. Symbolic Powers and other Contractions of Ideals in Noetherian Rings. [Doctoral Dissertation]. University of Michigan; 2012. Available from: http://hdl.handle.net/2027.42/94031