Work

On the determinants of matrices with elements from arbitrary sets

Year: 2025

Type: article

Abstract: Recently there have been several works estimating the number of matrices with elements from some finite sets of arithmetic interest and of a given determinant. Typically such results are compared with the trivial upper bound , where is the cardinality of . Here we show that even for arbitrary sets , some recent results from additive combinatorics enable us to obtain a stronger bound with a power saving.

Source: Mathematika

DOI: 10.1112/mtk.70018

Authors: Ilya D. Shkredov, Igor E. Shparlinski

Institutions: Purdue University West Lafayette, London Institute for Mathematical Sciences, UNSW Sydney

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Australian Research Council

Awards: Ubiquity of Kloosterman sums in Number Theory and Beyond, Pseudorandomness in Number Theory, Dynamics and Cryptography