First Moment of Quadratic Hecke $L$-Functions with Lower Order Term

Peng Gao; Liangyi Zhao

doi:10.1016/j.jnt.2026.04.008

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arXiv · 2512.22509

First Moment of Quadratic Hecke $L$-Functions with Lower Order Term

Peng Gao·Liangyi Zhao

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Abstract

We evaluate the first moment of the family of primitive quadratic Hecke $L$-functions in the Gaussian field using the method of double Dirichlet series under the Riemann hypothesis and the Lindel\"of hypothesis. We obtain asymptotic formulas with secondary main terms and error terms of size that is one quarter of that of the main term.

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BibTeX RIS

Peng Gao, Liangyi Zhao. 2025-12-27. First Moment of Quadratic Hecke $L$-Functions with Lower Order Term. https://doi.org/10.1016/j.jnt.2026.04.008

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