Work

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

Year: 2024

Type: article

Abstract: Let [Formula: see text] be the [Formula: see text]th Fourier coefficient of [Formula: see text] Hecke–Maass cusp form, denoted as [Formula: see text] or the triple divisor function, denoted as [Formula: see text]. Let [Formula: see text] be an integer. In this paper, we establish an asymptotic formula for the sum [Formula: see text] where [Formula: see text] is either von Mangoldt function or identity function, and [Formula: see text] is a binary quadratic polynomial. When [Formula: see text], then [Formula: see text] can be any bounded arithmetical function.

Source: International Journal of Number Theory

DOI: 10.1142/s1793042125500265

Authors: Himanshi Chanana, Saurabh Kumar Singh

Institution: Indian Institute of Technology Kanpur

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Indian Institute of Technology Kanpur, Department of Science and Technology, Ministry of Science and Technology, India, University Grants Commission

Awards: G2580309077, G5460774449