English

Generalized Euler constants

Number Theory 2019-05-01 v2

Abstract

We define a family {γ(P)\gamma(P)} of generalized Euler constants indexed by finite sets of primes PP and study their distribution. These arise from partial sums of reciprocals of integers not divisible by any prime in PP. An apparent monotonicity is investigated. We also prove that a certain property of these numbers is equivalent to the Riemann Hypothesis.

Keywords

Cite

@article{arxiv.math/0703508,
  title  = {Generalized Euler constants},
  author = {Harold G. Diamond and Kevin Ford},
  journal= {arXiv preprint arXiv:math/0703508},
  year   = {2019}
}

Comments

v2. 13 pages. Minor changes suggested by the referee. To appear in Math. Proc. Cambridge Phil. Soc