Let p be a prime. In this paper, we present detailed p-adic analysis to factorials and double factorials and their congruences. We give good bounds for the p-adic sizes of the coefficients of the divided universal Bernoulli number B̂n n when n is divisible by p−1. Using these we then establish the universal Kummer congruences modulo powers of a prime p for the divided universal Bernoulli numbers...

It has been argued that pension funds should have limitations on their asset allocation, based on the risk profile of the different financial instruments available on the financial markets. This issue proves to be highly relevant at times of market crisis, when a regulation establishing limits to risk taking for pension funds could prevent defaults. In this paper we present a framework for eval...

In this report we study the arithmetic of Rikuna’s generic polynomial for the cyclic group of order n and obtain a generalized Kummer theory. It is useful under the condition that ζ 6∈ k and ω ∈ k where ζ is a primitive n-th root of unity and ω = ζ + ζ−1. In particular, this result with ζ ∈ k implies the classical Kummer theory. We also present a method for calculating not only the conductor bu...

We calculate the automorphism groups of several Kummer surfaces associated with the product of two elliptic curves. We give their generators explicitly.

We study the a-numbers and p-ranks of Kummer covers of the projective line, and we give bounds for these numbers.

The classical Kummer construction attaches to an abelian surface a K3 surface. As Shioda and Katsura showed, this construction breaks down for supersingular abelian surfaces in characteristic two. Replacing supersingular abelian surfaces by the selfproduct of the rational cuspidal curve, and the sign involution by suitable infinitesimal group scheme actions, I give the correct Kummer-type const...

The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. In this paper, we introduce a generalization—referred to as the beta Gumbel distribution—generated from the logit of a beta random variable. We provide a comprehensive treatment of the mathematical properties of this new distribution. We derive the analytical shapes of the correspond...