Generalised Euler constants

Generalized Euler constants 3

We study the distribution of a family {γ(P)} of generalized Euler constants arising from integers sieved by finite sets of primes P . For P = Pr, the set of the first r primes, γ(Pr)→ exp(−γ) as r →∞. Calculations suggest that γ(Pr) is monotonic in r, but we prove it is not. Also, we show a connection between the distribution of γ(Pr) − exp(−γ) and the Riemann hypothesis.

Generalized Euler Constants

We define a family {γ(P)} of generalized Euler constants indexed by finite sets of primes P and study their distribution. An apparent monotonicity is investigated.

ε-constants and equivariant Arakelov Euler characteristics

Let R[G] be the group ring of a finite group G over a ring R. In this article, we study Euler characteristics of bounded metrised complexes of finitely generated Z[G]-modules, with applications to Arakelov theory and the determination of ǫ-constants. A metric on a bounded complex K• of finitely generated Z[G]-modules is specified by giving for each irreducible character φ of G a metric on the d...

Generalised Hermite Constants, Voronoi Theory and Heights on Flag Varieties

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...