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Low-lying zeros of quadratic Dirichlet L-functions: lower order terms for extended support

D. Fiorilli ; J. Parks ; Anders Södergren (Institutionen för matematiska vetenskaper)
Compositio Mathematica (0010-437X). Vol. 153 (2017), 6, p. 1196-1216.
[Artikel, refereegranskad vetenskaplig]

We study the 1-level density of low-lying zeros of Dirichlet L-functions attached to real primitive characters of conductor at most X. Under the generalized Riemann hypothesis, we give an asymptotic expansion of this quantity in descending powers of log X, which is valid when the support of the Fourier transform of the corresponding even test function phi is contained in (-2, 2). We uncover a phase transition when the supremum sigma of the support of (phi) over cap reaches 1, both in the main term and in the lower order terms. A new lower order term appearing at sigma = 1 involves the quantity (phi) over cap (1), and is analogous to a lower order term which was isolated by Rudnick in the function field case.

Nyckelord: zeros of L-functions, Katz-Sarnak heuristics, quadratic Dirichlet L-functions, 1-level density

Denna post skapades 2017-07-26. Senast ändrad 2017-10-03.
CPL Pubid: 250805


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