First moment of quadratic Dirichlet $L$-functions with secondary terms

Martin Čech

First moment of quadratic Dirichlet $L$-functions with secondary terms

Number Theory 2025-09-09 v2

Authors: Martin Čech

Abstract

We study the first moment of primitive quadratic Dirichlet $L$ -functions. Assuming the Riemann hypothesis and the generalized Lindel\"of hypothesis, we obtain an asymptotic formula at the central point with error $O(X^{1/4+\epsilon})$ , and identify lower-order terms of size $X^{1/3}\log X$ .

Keywords

column subset selection QR factorization sparse subspace embeddings rank-revealing leverage scores sketched matrix randomized algorithms

Cite

@article{arxiv.2509.03197,
  title  = {First moment of quadratic Dirichlet $L$-functions with secondary terms},
  author = {Martin Čech},
  journal= {arXiv preprint arXiv:2509.03197},
  year   = {2025}
}

Comments

Corrected title and other minor fixes; 34 pages

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