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L-Functions and Algebraic Varieties. A conference in memory of Alexey Zykin
7 февраля 2018 г. 12:30–13:30, Moscow, Moscow Independent University, 11 Bolshoi Vlassievsky per.
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Low-lying zeros of quadratic Dirichlet L-function: the transition
Daniel Fiorilli |
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Эта страница: | 173 | Видеофайлы: | 3 |
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Аннотация:
I will discuss recent joint work with James Parks and Anders Södergren. Looking at the one-level density of low-lying zeros of quadratic Dirichlet L-functions, Katz and Sarnak predicted a sharp transition in the main terms when the support of the Fourier transform of the implied test functions reaches the point 1. By estimating this quantity up to a power-saving error term, we show that such a transition is also present in lower-order terms. In particular this answers a question of Rudnick coming from the function field analogue. We also show that this transition is also present in the Ratios Conjecture's prediction.
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