In this paper we show how hypercomplex function theoretical objects can be used to construct explicitly self-dual SU(2)-Yang-Mills instanton solutions on certain classes of conformally flat 4-manifolds. We use a hypercomplex argument principle to establish a natural link between the fundamental solutions of D∆f = 0 and the second Chern class of the SU(2) principal bundles over these manifolds. ...

There are two kinds of L-functions, and they will be described below: motivic L-functions which generalize the Artin L-functions and are defined purely arithmetically, and automorphic L-functions, defined by data which are largely transcendental. Within the automorphic L-functions a special class can be singled out, the class of standard L-functions, which generalize the Hecke L-functions and f...

In this paper, we study the existence of weighted pseudo almost automorphic mild solutions of integro-differential equations with fractional order 1 < α < 2, here A is a linear densely defined operator of sectorial type on a complex Banach space X. This paper also deals with existence of weighted pseudo almost automorphic mild solutions of semilinear integro-differential eqautions with A is the...

We prove new modularity lifting theorems for p-adic Galois representations in situations where the methods of Wiles and Taylor–Wiles do not apply. Previous generalizations of these methods have been restricted to situations where the automorphic forms in question contribute to a single degree of cohomology. In practice, this imposes several restrictions – one must be in a Shimura variety settin...

In this article we shall give an elementary introduction to an important problem in representation theory. The problem is to relate the automorphic representations of classical groups to those of the general linear group. Thanks to the work of a number of people over the past twenty-five years, the automorphic representation theory of GL(n) is in pretty good shape. The theory for GL(n) now incl...

The first part of this report describes the class of representations of Galois groups of number fields that have been attached to automorphic representations. The construction is based on the program for analyzing cohomology of Shimura varieties developed by Langlands and Kottwitz. Using p-adic methods, the class of Galois representations obtainable in this way can be expanded slightly; the lin...

By using spectral expansions in global automorphic Levi–Sobolev spaces, we estimate an average of the first Fourier coefficients of Maass cusp forms for SL2(Z), producing a soft estimate on the first numerical Fourier coefficients of Maass cusp forms, which is an example of a general technique for estimates on compact periods via application of a pre–trace formula. Incidentally, this shows that...

Abstract We establish a result of Bombieri–Vinogradov type for the Dirichlet coefficients at prime ideals standard $L$-function associated to self-dual cuspidal automorphic representation $\pi $ $\operatorname {GL}_n$ over number field $F$ when $\pi$ is not quadratic twist itself. Our does rely on any unproven progress towards generalized Ramanujan conjecture or nonexistence Landau–Siegel zeros...