Discussion of theory and applications of algebraic curves over finite fields with many rational points.
These notes are intended as an introduction to those aspects of analytic number theory which depend on and have applications to the theory of algebraic numbers. The first part of these notes treats all the necessary local aspects of algebraic number theory that appear in the for…
These notes are intended as an introduction to those aspects of analytic number theory which depend on and have applications to the algebraic numbers. As is well known the central problem of the theory general algebraic formulation of ·the following distribution results: number …
Werke des deutschen Mathematikers Ernst Eduard Kummer, dessen Einführung von Idealzahlen, die als spezielle Untergruppe eines Rings definiert sind, den Grundsatz der Arithmetik (eindeutige Faktorisierung jeder ganzen Zahl zu einem Produkt von Primzahlen) auf komplexe Zahlenfelde…
This volume gives an introduction to the algebraic theory of Hecke algebras, which can be viewed as generalizations of group algebras. At first a careful look at the product leads to liftings of the basic isomorphism theorems and of anti-homomorphisms from the group level to the…
This memoir offers, via the Rankin-Selberg method, a thorough and comprehensive examination of the degree 16 standard L-function of the product of two rank two symplectic similitude groups, which includes the study of the global integral of Rankin Selberg type and local integral…
This work defines the higher spinor classes of an orthogonal representation of a Galois group. These classes are higher-degree analogues of the Fröhlich spinor class, which quantify the difference between the Stiefel-Whitney classes of an orthogonal representation and the Hasse-…
This memoir provides a detailed study of the effect of non power-like irregularities of (the geometry of) the fractal boundary on the spectrum of "fractal drums" (and especially of "fractal strings"). In this work, the authors extend previous results in this area by using the no…