Divisor function and bounds in domains with enough primes

Year 2019, Volume: 48 Issue: 2, 399 - 405, 01.04.2019

Haydar Göral

Abstract

In this note, first we show that there is no uniform divisor bound for the Bézout identity using Dirichlet's theorem on arithmetic progressions. Then, we discuss for which rings the absolute value bound for the Bézout identity is not trivial and the answer depends on the number of small primes in the ring.

Keywords

divisor function, arithmetic progression, polynomials, unique factorization domain

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