Work

Sums of products of Kloosterman sums to prime power moduli

Year: 2026

Type: article

Abstract: We prove new bounds on complete sums of products of $$k$$ k additively shifted Kloosterman sums to odd high prime power moduli $$q=p^n$$ q = p n , which feature substantially stronger power savings (about $$q^{-1/\lceil k/2\rceil}$$ q - 1 / ⌈ k / 2 ⌉ in generic configurations) and a novel quantification of the alignment among the shifts. We prove our bounds by developing a method to estimate complete exponential sums with a broad class of phases well-controlled by a specified number of initial terms in a property reflecting p -adic differentiability.

Source: Analysis Mathematica

DOI: 10.1007/s10476-026-00197-7

Authors: D. Milićević, C. Robinson, C. Shupe

Institutions: Bryn Mawr College, PA Consulting Group, Rice University

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: National Science Foundation