Euler–Lehmer constants and a conjecture of Erdös

New Criteria for Existence of a Class of Generalized Euler-types Constants

One of the most important mathematical constants is Euler-Mascheroni constant that is the limit of the sequence --------------------------------  and is denoted by gamma. Some other developed constants known as Euler type constants are introduced in order to generalize the above constant. In the present paper, inspired by the functional sequence derivative of the limit summand of functions (i...

Values of the Euler Φ-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields

Let φ 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 6 x such that q ∤ φ(n). Part of the analysis involves a careful study of the Euler-Kronecker constants for cyclotomic fields. In particular, we show that the Hardy-Littlewood conjecture about counts of prime k-tuples and a conjecture o...

The Graham Conjecture Implies the Erdös-turán Conjecture

Erdös and Turán once conjectured that any set A ⊂ N with

On the Erdös-Straus Conjecture: Properties of Solutions to its Underlying Diophantine Equation

Newton-Cotes integration for approximating Stieltjes (generalized Euler) constants

In the Laurent expansion ζ(s, a) = 1 s− 1 + ∞ ∑ k=0 (−1)γk(a) k! (s− 1) , 0 < a ≤ 1, of the Riemann-Hurwitz zeta function, the coefficients γk(a) are known as Stieltjes, or generalized Euler, constants. [When a = 1, ζ(s, 1) = ζ(s) (the Riemann zeta function), and γk(1) = γk.] We present a new approach to high-precision approximation of γk(a). Plots of our results reveal much structure in the gr...