Generalized Euler constants

Abstract

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

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

Cited by in corpus (4)

• The Erdos conjecture for primitive sets
• Shifted Euler constants and a generalization of Euler-Stieltjes constants
• Linear and algebraic independence of Generalized Euler-Briggs constants
• Transcendence of generalized Euler-Kronecker constants