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

Number Theory 2026-03-30 v2

Abstract

We evaluate the first moment of the family of primitive quadratic Hecke LL-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.

Keywords

Cite

@article{arxiv.2512.22509,
  title  = {First Moment of Quadratic Hecke $L$-Functions with Lower Order Term},
  author = {Peng Gao and Liangyi Zhao},
  journal= {arXiv preprint arXiv:2512.22509},
  year   = {2026}
}

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15 pages