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One-level density estimates for Dirichlet L-functions with extended support

Drappeau, Sary and Pratt, Kyle and Radziwiłł, Maksym (2020) One-level density estimates for Dirichlet L-functions with extended support. . (Unpublished)

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We estimate the 1-level density of low-lying zeros of L(s,χ) with χ ranging over primitive Dirichlet characters of conductor ∈[Q/2,Q] and for test functions whose Fourier transform is supported in [−2−50/1093,2+50/1093]. Previously any extension of the support past the range [−2,2] was only known conditionally on deep conjectures about the distribution of primes in arithmetic progressions, beyond the reach of the Generalized Riemann Hypothesis (e.g Montgomery's conjecture). Our work provides the first example of a family of L-functions in which the support is unconditionally extended past the "trivial range" that follows from a simple application of the underlying trace formula (in this case orthogonality of characters). We also highlight consequences for non-vanishing of L(s,χ).

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Additional Information:Part of this work was conducted while the second author was supported by the National Science Foundation Graduate Research Program under grant number DGE-1144245. The third author acknowledges the support of a Sloan fellowship and NSF grant DMS-1902063.
Funding AgencyGrant Number
NSF Graduate Research FellowshipDGE-1144245
Alfred P. Sloan FoundationUNSPECIFIED
Classification Code:2010 Mathematics Subject Classification. 11M50 (Primary); 11M50, 11N13 (Secondary)
Record Number:CaltechAUTHORS:20210825-184530218
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110526
Deposited By: George Porter
Deposited On:26 Aug 2021 14:51
Last Modified:26 Aug 2021 14:51

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