In this paper, by deriving an inequality involving the generating function of Bernoulli numbers, author introduces a new ratio finitely many gamma functions, finds complete monotonicity second logarithmic derivative ratio, and simply reviews several linear combinations digamma or trigamma functions.

In the paper, authors establish an inequality involving exponential functions and sums, introduce a ratio of finitely many gamma functions, discuss properties, including monotonicity, logarithmic convexity, (logarithmically) complete Bernstein function property, newly introduced ratio, construct two inequalities multinomial coefficients multivariate beta functions.

We prove that the theory of the p-adics Qp, together with a set of explicitly given sorts, admits elimination of imaginaries. Using p-adic integration, we deduce the rationality of certain formal zeta functions arising from definable equivalence relations. As an application, we prove rationality results for zeta functions obtained by counting isomorphism classes of irreducible representations o...

The local normal zeta functions of a finitely generated, torsion-free nilpotent group G of class 2 depend on the geometry of the Pfaffian hypersurface associated to the bilinear form induced by taking commutators in G. The smallest examples of zeta functions which are not finitely uniform arise from groups whose associated Pfaffian hypersurfaces are plane curves. In this paper we study groups w...