Divisor function and bounds in domains with enough primes

Authors : Haydar Göral

Pages : 399-405

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Publication Date : 2019-04-01

Article Type : Research

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