On Some Products Taken over Prime Numbers
Abdelmalek Bedhouche and Bakir Farhi
Laboratoire de Mathématiques appliquéees
Faculté des Sciences Exactes
Université de Bejaia
We study expressions of the type
is a nonnegative real number,
is an arithmetic function satisfying some conditions, and the product
is over the primes
. We begin by proving that such expressions can be
expressed by using the
function, without reference to
prime numbers; we illustrate this result with several examples. The rest
of the paper is devoted to studying two particular cases related
. In both cases, we find arithmetic
properties and analytic estimates for the underlying expressions.
Full version: pdf,
(Concerned with sequences
Received July 26 2022; revised versions received November 1 2022; December 15 2022.
Published in Journal of Integer Sequences,
January 2 2023.
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