Let $\phi $ denote Euler's phi function. For a fixed odd prime $ q $ we investigate the first
and second order terms of the asymptotic series expansion for the number of $ n\leqslant x …

Abstract The Brauer–Siegel theorem concerns the size of the product of the class number
and the regulator of a number field K. We derive bounds for this product in case K is a prime …

Using a new factor chain argument, we show that $5 $ does not divide an odd perfect
number indivisible by a sixth power. Applying sieve techniques, we also find an upper …

We give explicit numerical values with 100 decimal digits for the Mertens constant involved
in the asymptotic formula for 1/p and, as a byproduct, for the Meissel-Mertens constant …

What are the known Fermat primes? Hardy and Wright [HW] say that only four such primes
are known, but this is incorrect since taking Fn= 22n+ 1, as they did, F0, F1, F2, F3, and F4 …

Rosser and Schoenfeld remarked that the product∏ p≤ x (1− 1/p)− 1 exceeds e γ log x for
all 2≤ x≤ 1 0 8, and raised the question whether the difference changes sign infinitely …

Euler constants from primes in arithmetic progression Page 1 MATHEMATICS OF
COMPUTATION https://doi.org/10.1090/mcom/4057 Article electronically published on January …

ON THE CONSTANT IN THE MERTENS PRODUCT FOR ARITHMETIC PROGRESSIONS. I.
IDENTITIES Alessandro Languasco, Alessandro Zaccagnini 1. Page 1 Functiones et …

Motivated by their research on automorphism groups of pseudo-real Riemann surfaces,
Bujalance, Cirre and Conder have conjectured that there are infinitely many primes $ p …

A 1976 result from Norton may be used to give an asymptotic (but not explicit) description of
the constant in Mertens' second theorem for primes in arithmetic progres-sions. Assuming …