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University of Toronto

1. Dahl, Alexander Oswald. Subconvexity for a Twisted Double Dirichlet Series and Non-vanishing of L-functions.

Degree: PhD, 2015, University of Toronto

We study a double Dirichlet series of the form ∑d L(s,χd χ)χ'(d)d-w , where χ and χ' are quadratic Dirichlet characters with prime conductors N and M respectively. A functional equation group isomorphic to the dihedral group of order 6 continues the function meromorphically to ℂ2. A convexity bound at the central point is established to be (MN)3/8+ε and a subconvexity bound of (MN(M+N))1/6+ε is proven. This bound is used to prove an upper bound for the smallest positive integer d such that L(1/2;χdN) does not vanish. Advisors/Committee Members: Blomer, Valentin, Mathematics.

Subjects/Keywords: analytic number theory; double Dirichlet series; L-functions; non-vanishing; subconvexity; 0405

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

APA (6th Edition):

Dahl, A. O. (2015). Subconvexity for a Twisted Double Dirichlet Series and Non-vanishing of L-functions. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/70922

Chicago Manual of Style (16th Edition):

Dahl, Alexander Oswald. “Subconvexity for a Twisted Double Dirichlet Series and Non-vanishing of L-functions.” 2015. Doctoral Dissertation, University of Toronto. Accessed July 10, 2020. http://hdl.handle.net/1807/70922.

MLA Handbook (7th Edition):

Dahl, Alexander Oswald. “Subconvexity for a Twisted Double Dirichlet Series and Non-vanishing of L-functions.” 2015. Web. 10 Jul 2020.

Vancouver:

Dahl AO. Subconvexity for a Twisted Double Dirichlet Series and Non-vanishing of L-functions. [Internet] [Doctoral dissertation]. University of Toronto; 2015. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/1807/70922.

Council of Science Editors:

Dahl AO. Subconvexity for a Twisted Double Dirichlet Series and Non-vanishing of L-functions. [Doctoral Dissertation]. University of Toronto; 2015. Available from: http://hdl.handle.net/1807/70922

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