Approximations of $SL(3,\mathbb{Z})$ Hecke-Maass $L$-Functions by short Dirichlet polynomials

Jiseong Kim

Approximations of $SL(3,\mathbb{Z})$ Hecke-Maass $L$-Functions by short Dirichlet polynomials

Number Theory 2026-01-21 v6

Authors: Jiseong Kim

Abstract

We study averages of $L$ -functions associated with Hecke-Maass cusp forms for $SL(3,\mathbb{Z})$ , multiplied by Dirichlet polynomials built from the Fourier coefficients of the cusp forms. To prove this, we employ a variant of the Kuznetsov trace formula. In particular, we show that the reciprocals of these $L$ -functions can be approximated by very short Dirichlet polynomials, on average over $t$ and over the forms.

Keywords

Hecke-Maass L-functions Dirichlet polynomials SL(3,Z) Kuznetsov trace formula cusp forms

Cite

@article{arxiv.2204.12612,
  title  = {Approximations of $SL(3,\mathbb{Z})$ Hecke-Maass $L$-Functions by short Dirichlet polynomials},
  author = {Jiseong Kim},
  journal= {arXiv preprint arXiv:2204.12612},
  year   = {2026}
}

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