Arithmetic Gevrey Series and Transcendence. a Survey
نویسنده
چکیده
منابع مشابه
Microsolutions of differential operators and values of arithmetic Gevrey series
We continue our investigation of E-operators, in particular their connection with G-operators; these differential operators are fundamental in understanding the diophantine properties of Siegel’s E and G-functions. We study in detail microsolutions (in Kashiwara’s sense) of Fuchsian differential operators, and apply this to the construction of basis of solutions at 0 and∞ of any E-operator from...
متن کاملThe Arithmetic and Geometry of Elliptic Surfaces
We survey some aspects of the theory of elliptic surfaces and give some results aimed at determining the Picard number of such a surface. For the surfaces considered, this will be equivalent to determining the Mordell-Weil rank of an elliptic curve defined over a function field in one variable. An interesting conjecture concerning Galois actions on the relative de Rham cohomology of these surfa...
متن کاملL - Series and Transcendental Numbers
This paper is a survey of some recent work of mine done jointly with V. Kumar Murty, N. Saradha, S. Gun and P. Rath. In all of these works, the motivating question is the following. Given an automorphic representation π , we consider the L-series L(s, π) attached to π according to the Langlands formalism. We are interested in the possible transcendence of special values L(k, π) when k is a posi...
متن کاملTranscendence in Positive Characteristic and Special Values of Hypergeometric Functions
We prove a simple transcendence criterion suitable for function field arithmetic. We apply it to show the transcendence of special values at non-zero rational arguments (or more generally, at algebraic arguments which generate extension of the rational function field with less than q places at infinity) of the entire hypergeometric functions in the function field (over Fq) context, and to obtai...
متن کاملAutomata Methods in Transcendence
The purpose of this expository article is to explain diverse new tools that automata theory provides to tackle transcendence problems in function field arithmetic. We collect and explain various useful results scattered in computer science, formal languages, logic literature and explain how they can be fruitfully used in number theory, dealing with transcendence, refined transcendence and class...
متن کامل