Approximations of SL(3,ℤ) Hecke-Maass L-Functions by short Dirichlet polynomials

2022/04/26 by Jiseong Kim, Kim, Jiseong
Mathematics · #11F30 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2204.12612

openalex publication_date 2022/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We study averages of L-functions associated with Hecke-Maass cusp forms for SL(3,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.

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