Related papers: Geometrization of Trace Formulas
The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After…
The geometric Langlands correspondence for function fields over finite fields has been proved by Frenkel, Gaitsgory, Vilonen. The aim of this article is to write translation for curves over the complex field and prove the correspondence in…
We provide a generalization of an algebraic linear combination for the trace of certain elliptic modular forms, and through specializing the expression at a suitable pair consisting of an elliptic curve over algebraic number fields and its…
Many product formulas are known classically for generalized hypergeometric functions over the complex numbers. In this paper, we establish some analogous formulas for generalized hypergeometric functions over finite fields.
The Langlands correspondence for complex curves is traditionally formulated in terms of sheaves rather than functions. Recently, Langlands asked whether it is possible to construct a function-theoretic version. In this paper we use the…
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…
We investigate geometric properties of a class of trace functions expressed in terms of the deformed logarithmic and exponential functions. These trace functions and their properties may be of independent interest. We use them in particular…
The trace formula constitutes a fundamental tool in the Langlands program. In general, Arthur introduced a truncation operator to render both the geometric and spectral sides of the formula convergent. This paper focuses on the case of…
We show that formulas differing from classical analogues of rational trace formulas for algebraic-geometric potentials occur in the theory of finite-gap integration of spectral equations. The new formulas contain transcendental modular…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
The geometry of algebraic curves over finite fields is a rich area of research. In previous work, the authors investigated a particular aspect of the geometry over finite fields of the classical unit circle, namely how the number of…
Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are…
We introduce a novel formulation for geometry on discrete points. It is based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions. We expand this mathematical framework so…
In this note is we exhibit an elementary method to construct explicitly curves over finite fields with many points. Despite its elementary character the method is very efficient and can be regarded as a partial substitute for the use of…
We establish endoscopic and stable trace formulas whose discrete spectral terms are weighted by automorphic $L$-functions, by the use of basic functions that are incorporated into the global spectral and geometric coefficients. This is a…
Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
The geometric Langlands correspondence for complex algebraic curves differs from the original Langlands correspondence for number fields in that it is formulated in terms of sheaves rather than functions (in the intermediate case of curves…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of…