On the third moment of L(\tfrac12, χ_d) II: the number field case

2018/04/02 by Adrian Diaconu, Diaconu, Adrian, Ian Whitehead +1
Mathematics · #11M32 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1804.00690

openalex publication_date 2018/04/02 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

We establish a smoothed asymptotic formula for the third moment of quadratic Dirichlet L-functions at the central value. In addition to the main term, which is known, we prove the existence of a secondary term of size x^(3)/(4). The error term in the asymptotic formula is on the order of O(x^(2)/(3)+δ) for every δ> 0.

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