Chinese Quarterly Journal of Mathematics ›› 2025, Vol. 40 ›› Issue (4): 360-371.doi: 10.13371/j.cnki.chin.q.j.m.2025.04.003

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Moments of Dirichlet L-Functions

  

  1. Data Science Institute and School of Mathematics, Shandong University, Jinan 250100, China
  • Received:2025-08-26 Online:2025-12-30 Published:2025-12-30
  • About author:HUANG Bing-rong, professor of Shandong University, engages in analytic number theory; HUANG Jun-hao, master student of Shandong University, engages in analytic number theory.
  • Supported by:
    Supported by the National Key R&D Program of China (Grant No. 2021YFA1000700) and National Natural Science Foundation of China (Grant No. 12031008).

Abstract: In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. Our main tool is a power-saving estimate of bilinear forms of hyper-Kloosterman sums due to Kowalski–Michel–Sawin.

Key words: Moment, Twist, Dirichlet L-functions, Coset

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