Sum of the $GL(3)$ Fourier coefficients over quadratics and mixed powers

Himanshi Chanana; Saurabh Kumar Singh

Sum of the $GL(3)$ Fourier coefficients over quadratics and mixed powers

Number Theory 2023-10-18 v1

Authors: Himanshi Chanana , Saurabh Kumar Singh

Abstract

Let $\Lambda(1,n)$ be the $(1,n)$ -th Fourier coefficients of $SL(3,\mathbb{Z})$ Hecke-Maass cusp form and $d_3(n)$ denotes the triple divisor function. This paper establishes non-trivial bounds for the averages of these arithmetic functions over polynomials in three variables having mixed powers and over quadratic forms.

Keywords

fourier coefficients hecke-maass cusp form triple divisor function quadratic forms mixed powers analytic number theory

Cite

@article{arxiv.2310.11408,
  title  = {Sum of the $GL(3)$ Fourier coefficients over quadratics and mixed powers},
  author = {Himanshi Chanana and Saurabh Kumar Singh},
  journal= {arXiv preprint arXiv:2310.11408},
  year   = {2023}
}

Comments

30 pages. arXiv admin note: substantial text overlap with arXiv:2303.15856

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