In this note we give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger’s theorem.

In this paper, we give asymptotic formulas for the number of cyclic quartic extensions of a number field. 1. Galois, Kummer, and Hecke Theory 1.

Stefan Kummer: Kunstgeschichte der Stadt Würzburg 800–1945. Regensburg (Schnell und Steiner) 2011. 288 S., Abb.

The hypergeometric differential equation was found by Euler [Euler, L. (1769) Opera Omnia Ser. 1, 11-13] and was extensively studied by Gauss [Gauss, C. F. (1812) Comm. Soc. Reg. Sci. II 3, 123-162], Kummer [Kummer, E. J. (1836) Riene Ang. Math. 15, 39-83; Kummer, E. J. (1836) Riene Ang. Math. 15, 127-172], and Riemann [Riemann, B. (1857) K. Gess. Wiss. 7, 1-24]. The hypergeometric function kno...

In the research presented in this paper, confluent hypergeometric function is embedded theory of strong differential superordinations. order to proceed with study, form adapted taking into consideration certain classes analytic functions depending on an extra parameter previously introduced related subordination and superordination. Operators defined using function, namely Kummer–Bernardi Kumme...

In this note we give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger’s theorem.

Abstract We prove that there is a positive proportion of L -functions associated to cubic characters over $\mathbb F_q[T]$ do not vanish at the critical point $s=1/2$ . This achieved by computing first mollified moment using techniques previously developed authors in their work on -functions, and obtaining sharp upper bound for second moment, building Lester Radziwi??, which turn develops furth...

We discuss a generalization of Kummer construction which, on the base of an integral representation of a finite group and local resolution of its quotient, produces a higher dimensional variety with trivial canonical class. We use virtual Poincaré polynomials with coefficients in a ring of representations and McKay correspondence to compute cohomology of such Kummer varieties. 1. The constructi...

Let SUC(2, L) denote the projective moduli variety of semistable rank 2 vector bundles with determinant L ∈ Pic(C) on a smooth curve C of genus g > 2; and suppose that degL is even. It is well-known that, on the one hand, the singular locus of SUC(2, L) is isomorphic to the Kummer variety of the Jacobian; and on the other hand that when C is nonhyperelliptic SUC(2,O) has an injective morphism i...