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University of Illinois – Urbana-Champaign

1. Xiao, Jiajie. Distribution of some arithmetic sequences.

Degree: PhD, 0439, 2013, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/45594

► In this thesis, we first study the correlations of some arithmetic sequences. We prove the existence of the limiting pair correlations of fractions with prime…
(more)

Subjects/Keywords: Number theory; analytic number theory.

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

APA (6^{th} Edition):

Xiao, J. (2013). Distribution of some arithmetic sequences. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/45594

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

Xiao, Jiajie. “Distribution of some arithmetic sequences.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed August 18, 2019. http://hdl.handle.net/2142/45594.

MLA Handbook (7^{th} Edition):

Xiao, Jiajie. “Distribution of some arithmetic sequences.” 2013. Web. 18 Aug 2019.

Vancouver:

Xiao J. Distribution of some arithmetic sequences. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2019 Aug 18]. Available from: http://hdl.handle.net/2142/45594.

Council of Science Editors:

Xiao J. Distribution of some arithmetic sequences. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/45594

University of Illinois – Urbana-Champaign

2. Spiegelhalter, Paul. Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/50445

► K.T. Atanassov introduced the two arithmetic functions [ I(n) = \prod_{ν=1}^{k} p_ν^{1/α_ν} {and} R(n) = \prod_{ν=1}^{k} p_ν^{αv - 1} ] called the irrational factor and…
(more)

Subjects/Keywords: Number theory; Dirichlet series; Farey fractions

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

APA (6^{th} Edition):

Spiegelhalter, P. (2014). Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/50445

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

Spiegelhalter, Paul. “Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed August 18, 2019. http://hdl.handle.net/2142/50445.

MLA Handbook (7^{th} Edition):

Spiegelhalter, Paul. “Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations.” 2014. Web. 18 Aug 2019.

Vancouver:

Spiegelhalter P. Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2019 Aug 18]. Available from: http://hdl.handle.net/2142/50445.

Council of Science Editors:

Spiegelhalter P. Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/50445

University of Illinois – Urbana-Champaign

3. Anders, Katherine. Properties of digital representations.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/50698

► Let 𝓐 be a finite subset of ℕ including 0 and f_𝓐(n) be the number of ways to write n=∑_{i=0}^{∞}ε_{i2}^{i}, where ε_{i}∈𝓐. The sequence ≤ ft(f_𝓐(n)))…
(more)

Subjects/Keywords: number theory; combinatorics; digital representations; generalized binary representations

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

APA (6^{th} Edition):

Anders, K. (2014). Properties of digital representations. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/50698

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

Anders, Katherine. “Properties of digital representations.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed August 18, 2019. http://hdl.handle.net/2142/50698.

MLA Handbook (7^{th} Edition):

Anders, Katherine. “Properties of digital representations.” 2014. Web. 18 Aug 2019.

Vancouver:

Anders K. Properties of digital representations. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2019 Aug 18]. Available from: http://hdl.handle.net/2142/50698.

Council of Science Editors:

Anders K. Properties of digital representations. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/50698

University of Illinois – Urbana-Champaign

4. Tangjai, Wipawee. Density and spacing properties of some families of non-standard ternary representations.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/50750

► In this dissertation, we study a family of non-standard digital representations in base 3. Let A be an index set such that A={0,u1,u2}, where u1…
(more)

Subjects/Keywords: Combinatorial number theory; Digital representation; non-standard digit sets; ternary representations; generating functions; sequences; subsets of integers

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

APA (6^{th} Edition):

Tangjai, W. (2014). Density and spacing properties of some families of non-standard ternary representations. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/50750

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

Tangjai, Wipawee. “Density and spacing properties of some families of non-standard ternary representations.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed August 18, 2019. http://hdl.handle.net/2142/50750.

MLA Handbook (7^{th} Edition):

Tangjai, Wipawee. “Density and spacing properties of some families of non-standard ternary representations.” 2014. Web. 18 Aug 2019.

Vancouver:

Tangjai W. Density and spacing properties of some families of non-standard ternary representations. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2019 Aug 18]. Available from: http://hdl.handle.net/2142/50750.

Council of Science Editors:

Tangjai W. Density and spacing properties of some families of non-standard ternary representations. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/50750

University of Illinois – Urbana-Champaign

5. Kim, Eunmi. Root distribution of polynomials and distance sums on the unit circle.

Degree: PhD, 0439, 2013, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/44453

► Our first topic is the study of self-inversive polynomials. We establish sufficient conditions for self-inversive polynomials to have all zeros on the unit circle. We…
(more)

Subjects/Keywords: self-inversive polynomials; distance sum; unit circle

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

APA (6^{th} Edition):

Kim, E. (2013). Root distribution of polynomials and distance sums on the unit circle. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/44453

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

Kim, Eunmi. “Root distribution of polynomials and distance sums on the unit circle.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed August 18, 2019. http://hdl.handle.net/2142/44453.

MLA Handbook (7^{th} Edition):

Kim, Eunmi. “Root distribution of polynomials and distance sums on the unit circle.” 2013. Web. 18 Aug 2019.

Vancouver:

Kim E. Root distribution of polynomials and distance sums on the unit circle. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2019 Aug 18]. Available from: http://hdl.handle.net/2142/44453.

Council of Science Editors:

Kim E. Root distribution of polynomials and distance sums on the unit circle. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/44453

6. Ekvittayaniphon, Sakulbuth. On sequences related to binary partition function and the Thue-Morse sequence.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101563

► In this dissertation, we discuss properties of the family of sequences \mathbf{u_{d}} = {u_{d}(n)}_{n ≥ 0} for positive integer d. We define them by letting…
(more)

Subjects/Keywords: Binary Partition; Function; Thue-Morse Sequence

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

APA (6^{th} Edition):

Ekvittayaniphon, S. (2018). On sequences related to binary partition function and the Thue-Morse sequence. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101563

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

Ekvittayaniphon, Sakulbuth. “On sequences related to binary partition function and the Thue-Morse sequence.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed August 18, 2019. http://hdl.handle.net/2142/101563.

MLA Handbook (7^{th} Edition):

Ekvittayaniphon, Sakulbuth. “On sequences related to binary partition function and the Thue-Morse sequence.” 2018. Web. 18 Aug 2019.

Vancouver:

Ekvittayaniphon S. On sequences related to binary partition function and the Thue-Morse sequence. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2019 Aug 18]. Available from: http://hdl.handle.net/2142/101563.

Council of Science Editors:

Ekvittayaniphon S. On sequences related to binary partition function and the Thue-Morse sequence. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101563

7. Polanco Encarnacion, Geremias. Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/34298

► This dissertation is divided into three main sections. The main result of Section 1 is that, for a,b>1, irrational, the quantity log (a/b) is ``not…
(more)

Subjects/Keywords: Beatty Sequence; Sturmian Sequence; characteristic Sequence; Frullani's integral; Steinhaus Theorem; Three Gap Theorem; Kloosterman Sums; Farey Fractions

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

APA (6^{th} Edition):

Polanco Encarnacion, G. (2012). Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/34298

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

Polanco Encarnacion, Geremias. “Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed August 18, 2019. http://hdl.handle.net/2142/34298.

MLA Handbook (7^{th} Edition):

Polanco Encarnacion, Geremias. “Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory.” 2012. Web. 18 Aug 2019.

Vancouver:

Polanco Encarnacion G. Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2019 Aug 18]. Available from: http://hdl.handle.net/2142/34298.

Council of Science Editors:

Polanco Encarnacion G. Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/34298

8. Dixit, Atul. Transformation formulas associated with integrals involving the Riemann Ξ-function and rank-crank type PDEs in partition theory.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/34352

► There are two parts to this thesis. The first part deals with obtaining ``modular''-type transformation formulas involving various special functions such as the digamma function,…
(more)

Subjects/Keywords: Ramanujan; Riemann zeta function; Hurwitz zeta function; Bessel function; Koshliakov; Hardy; Ferrar; Rank-Crank partial differential equation (Rank-Crank PDE); Partition; $q$-series; Eisenstein series; Appell function

Record Details Similar Records

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

APA (6^{th} Edition):

Dixit, A. (2012). Transformation formulas associated with integrals involving the Riemann Ξ-function and rank-crank type PDEs in partition theory. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/34352

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

Dixit, Atul. “Transformation formulas associated with integrals involving the Riemann Ξ-function and rank-crank type PDEs in partition theory.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed August 18, 2019. http://hdl.handle.net/2142/34352.

MLA Handbook (7^{th} Edition):

Dixit, Atul. “Transformation formulas associated with integrals involving the Riemann Ξ-function and rank-crank type PDEs in partition theory.” 2012. Web. 18 Aug 2019.

Vancouver:

Dixit A. Transformation formulas associated with integrals involving the Riemann Ξ-function and rank-crank type PDEs in partition theory. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2019 Aug 18]. Available from: http://hdl.handle.net/2142/34352.

Council of Science Editors:

Dixit A. Transformation formulas associated with integrals involving the Riemann Ξ-function and rank-crank type PDEs in partition theory. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/34352

9. Tran, Khang. Discriminants: calculation, properties, and connection to the root distribution of polynomials with rational generating functions.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/34354

► This research centers on discriminants and how discriminants and their q-analogues relate to the root distribution of polynomials. This topic includes the connections between the…
(more)

Subjects/Keywords: discriminant; resultant; root distribution

Record Details Similar Records

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

APA (6^{th} Edition):

Tran, K. (2012). Discriminants: calculation, properties, and connection to the root distribution of polynomials with rational generating functions. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/34354

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

Tran, Khang. “Discriminants: calculation, properties, and connection to the root distribution of polynomials with rational generating functions.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed August 18, 2019. http://hdl.handle.net/2142/34354.

MLA Handbook (7^{th} Edition):

Tran, Khang. “Discriminants: calculation, properties, and connection to the root distribution of polynomials with rational generating functions.” 2012. Web. 18 Aug 2019.

Vancouver:

Tran K. Discriminants: calculation, properties, and connection to the root distribution of polynomials with rational generating functions. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2019 Aug 18]. Available from: http://hdl.handle.net/2142/34354.

Council of Science Editors:

Tran K. Discriminants: calculation, properties, and connection to the root distribution of polynomials with rational generating functions. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/34354

10. Vandehey, Joseph. Error term improvements for van der Corput transforms.

Degree: PhD, 0439, 2013, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/44398

► We improve the error term in the van der Corput transform for exponential sums, ∑ g(n) exp(2 π i f(n)). For many smooth functions g…
(more)

Subjects/Keywords: Asymptotic analysis; exponential sum; trigonometric sum; van der Corput transform

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

APA (6^{th} Edition):

Vandehey, J. (2013). Error term improvements for van der Corput transforms. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/44398

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

Vandehey, Joseph. “Error term improvements for van der Corput transforms.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed August 18, 2019. http://hdl.handle.net/2142/44398.

MLA Handbook (7^{th} Edition):

Vandehey, Joseph. “Error term improvements for van der Corput transforms.” 2013. Web. 18 Aug 2019.

Vancouver:

Vandehey J. Error term improvements for van der Corput transforms. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2019 Aug 18]. Available from: http://hdl.handle.net/2142/44398.

Council of Science Editors:

Vandehey J. Error term improvements for van der Corput transforms. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/44398

11. Reuter, Victoria. Hypergeometric functions, continued fractions for products of gamma functions, and q-analogues.

Degree: PhD, 0439, 2015, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/72779

► Some of the most interesting of Ramanujan's continued fraction identities are those involving ratios of Gamma functions in Chapter 12 of his second notebook. This…
(more)

Subjects/Keywords: hypergeometric functions; continued fractions; gamma function; basic hypergeometric functions; q-analogue; q-series; Ramanujan; Ramanujan's notebooks

Record Details Similar Records

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

APA (6^{th} Edition):

Reuter, V. (2015). Hypergeometric functions, continued fractions for products of gamma functions, and q-analogues. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/72779

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

Reuter, Victoria. “Hypergeometric functions, continued fractions for products of gamma functions, and q-analogues.” 2015. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed August 18, 2019. http://hdl.handle.net/2142/72779.

MLA Handbook (7^{th} Edition):

Reuter, Victoria. “Hypergeometric functions, continued fractions for products of gamma functions, and q-analogues.” 2015. Web. 18 Aug 2019.

Vancouver:

Reuter V. Hypergeometric functions, continued fractions for products of gamma functions, and q-analogues. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2015. [cited 2019 Aug 18]. Available from: http://hdl.handle.net/2142/72779.

Council of Science Editors:

Reuter V. Hypergeometric functions, continued fractions for products of gamma functions, and q-analogues. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2015. Available from: http://hdl.handle.net/2142/72779