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.

As of late, the study Fractional Calculus (FC) and Special Functions (SFs) has been interestingly prompted in various realms mathematics, engineering sciences. This is due to considerable demonstrated potential their applications. Among these SFs, Gamma function Mittag-Leffler functions are most renowned distinguished. Numerous authors continue this line. The current analysis attempts introduce...

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...