Nikulin proved that the isometries induced on the second cohomology group of a K3 surface X by a finite abelian group G of symplectic automorphisms are essentially unique. Moreover he computed the discriminant of the sublattice of H(X,Z) which is fixed by the isometries induced by G. However for certain groups these discriminants are not the same of those found for explicit examples. Here we de...

Keywords: Squared spherical Bessel functions Regularization of Hankel series Gaussian power-law densities Kummer distributions Airy approximation of Bessel integrals a b s t r a c t Bessel integrals of type R 1 0 k lþ2 e Àak 2 ÀðbþixÞk j 2 l ðpkÞdk are studied, where the squared spherical Bessel function j 2 l is averaged with a modulated Gaussian power-law density. These inte-grals define the ...

We develop a general classification theory for Brumer’s dihedral quintic polynomials by means of Kummer theory arising from certain elliptic curves. We also give a similar theory for cubic polynomials.

We establish an isomorphism between the quintic cyclic polynomials discovered by Hashimoto-Tsunogai and those arising from Kummer theory for certain algebraic tori. This enables us to solve the isomorphism problem for Hashimoto-Tsunogai polynomials and also Brumer’s quintic polynomials.

Using the representation of Eq(2) on the non-commutative space zz ∗−qz∗z = σ; q < 1, σ > 0 summation formulas for the product of two, three and four q-Kummer functions are derived.

Forschungen zur Bau- und Ausstattungsgeschichte von Kloster Bronnbach. Hrsg. HelmutFlachenecker, Stefan Kummer Monika Schaupp. Veröffentlichungen des Historischen Vereins Wertheim 9. (Verlag e.V.) 2014. 327 S., Abb.

We compare the Kummer flat (resp. etale) cohomology with coefficients in smooth commutative group schemes, finite schemes and logarithmic multiplicative of Kato. will be particularly interested case algebraic tori topology. also make some computations for certain special cases base log scheme.