Work

The second moment of sums of Hecke eigenvalues II

Year: 2026

Type: article

Abstract: Let be a holomorphic Hecke cusp form of weight for , and let denote its sequence of normalised Hecke eigenvalues. We compute the first and second moments of the sums , on average over forms of large weight . In the range , the size of the second moment lies between and . This is in sharp contrast to the regime , where the second moment was shown in preceding work (part I) to be of size .

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70519

Author: Ned Carmichael

Institution: King's College London

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Engineering and Physical Sciences Research Council, Heilbronn Institute for Mathematical Research