Work

Moments of Gaussian periods and modified Fermat curves

Year: 2025

Type: article

Abstract: We use supercharacter theory to study moments of Gaussian periods. For $$p-1=dk$$ p - 1 = d k and fixed k, we compute the fourth absolute moments for all but finitely many primes p. For d fixed, we relate the fourth absolute moments to the number of rational points on modified Fermat curves. For small d, this relation is in terms of a single curve. For larger d, we provide both exact formulas using families of modified Fermat curves and bounds via Hasse–Weil.

Source: The Ramanujan Journal

DOI: 10.1007/s11139-025-01090-x

Authors: Stephan Ramon Garcia, Brian Lorenz, George Todd

Institutions: Pomona College, University of California, Berkeley, University of Dayton

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Pomona College