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arxiv: 1105.1177 · v1 · pith:WROVJSF5new · submitted 2011-05-05 · 🧮 math.NT

Critical zeros of Dirichlet L-functions

Brian Conrey , Henryk Iwaniec , Kannan Soundararajan This is my paper
classification 🧮 math.NT
keywords criticaldirichletzerosasymptoticboundscharactersdegreefixed
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We use the Asymptotic Large Sieve and Levinson's method to obtain lower bounds for the proportion of simple zeros on the critical line of the twists by primitive Dirichlet characters of a fixed L-function of degree 1,2, or 3.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Low-Lying Zeros on the Critical Line for Families of Dirichlet $L$-Functions

    math.NT 2026-05 unverdicted novelty 6.0

    For large prime P and T at least on the order of 1 over sqrt(log P), the summed count of low-lying zeros on the critical line over characters mod P satisfies sum N0(T, chi) much greater than T squared P sqrt(log P).

  2. Low-Lying Zeros on the Critical Line for Families of Dirichlet $L$-Functions

    math.NT 2026-05 unverdicted novelty 5.0

    For large prime P and T at least order 1/sqrt(log P), the total number of low-lying zeros on the critical line summed over all characters mod P is at least order T squared P sqrt(log P).