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arxiv: 0708.2699 · v1 · submitted 2007-08-20 · 🧮 math.NT

The mean-square of Dirichlet L-functions

J. Brian Conrey This is my paper
classification 🧮 math.NT
keywords dirichletl-functionsmodulusprimecfkrscharactercompositeconjecture
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We verify the conjecture of [CFKRS] for the mean square near the critical point of Dirichlet L-functions for a composite modulus q. We also prove a kind of reciprocity formula when the second moment for a prime modulus is twisted by a character evaluated at a different prime.

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  1. Asymptotic second moment of Dirichlet $L$-functions along a thin coset

    math.NT 2023-12 unverdicted novelty 7.0

    Asymptotic formula with power-saving error for the second moment of Dirichlet L-functions on thin cosets of characters, featuring a secondary main term of size roughly q^{1/2} not predicted by the CFKRS conjecture.