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The second and third moment of L(1/2,χ) in the hyperelliptic ensemble

  • Alexandra Florea EMAIL logo
Published/Copyright: August 30, 2016

Abstract

We obtain asymptotic formulas for the second and third moment of quadratic Dirichlet L-functions at the critical point, in the function field setting. We fix the ground field 𝔽q, and assume for simplicity that q is a prime with q1(mod 4). We compute the second and third moment of L(1/2,χD), when D is a monic square-free polynomial of degree 2g+1, as g. The answer we get for the second moment agrees with Andrade and Keating’s conjectured formula in [4]. For the third moment, we check that the leading term agrees with the conjecture.

MSC 2010: 11M06; 11M38

Communicated by Jörg Brüdern


Acknowledgements

I would like to thank Kannan Soundararajan for his suggestions and for the many helpful discussions we have had while working on this problem. I would also like to thank the anonymous referees for their valuable comments and suggestions.

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Received: 2015-8-7
Revised: 2015-12-24
Published Online: 2016-8-30
Published in Print: 2017-7-1

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