Publication date
December 2010
DOI Publisher
Elsevier Inc. ISSN
0022-314X Citation count (estimate)
15Abstract
AbstractThe Euler–Lehmer constants γ(a,q) are defined as the limitslimx→∞(∑n⩽xn≡a(modq)1n−logxq). We show that at most one number in the infinite listγ(a,q),1⩽a<q,q⩾2, is an algebraic number. The methods used to prove this theorem can also be applied to study the following question of Erdös. If f:Z/qZ→Q is such that f(a)=±1 and f(q)=0, then Erdös conjectured that∑n=1∞f(n)n≠0. If q≡3(mod4), we show that the Erdös conjecture is true
Add to ORKG