Determinants related to Dirichlet characters modulo 2, 4 and 8 of binomial coefficients and the algebra of recurrence matrices

TL;DR

This paper investigates determinants associated with binomial coefficients evaluated on Dirichlet characters modulo 2, 4, and 8, utilizing recurrence matrices to analyze their algebraic properties.

Contribution

It introduces a novel approach using recurrence matrices to study determinants linked to binomial coefficients and Dirichlet characters modulo small integers.

Findings

Determinants exhibit specific algebraic structures related to Dirichlet characters

Recurrence matrices effectively analyze binomial coefficient evaluations

New relationships between determinants and algebra of recurrence matrices

Abstract

Using recurrence matrices, defined and described with some details, we study a few determinants related to evaluations of binomial coefficients on Dirichlet characters modulo 2, 4 and 8.