• Algebraic values of analytic f...

Result: Algebraic values of analytic functions

Title:
Algebraic values of analytic functions
Authors:
WALDSCHMIDT, Michel
Source:
Proceedings of the International Conference on Special Functions and their Applications, IMSc, Chennai, India, 23-27 September 2002, dedicated to Professor K. Srinivasa Rao on the occasion of his 60th birthdayJournal of computational and applied mathematics. 160(1-2):323-333
Publisher Information:
Amsterdam: Elsevier, 2003.
Publication Year:
2003
Physical Description:
print, 21 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Algèbre, Algebra, Théorie des nombres, Number theory, Analyse mathématique, Mathematical analysis, Fonctions d'une variable complexe, Functions of a complex variable, Fonctions de plusieurs variables complexes et espaces analytiques, Several complex variables and analytic spaces, Calcul scientifique, Scientific computation, Computación científica, Fonction analytique, Analytical function, Función analítica, Fonction n variables, N variable function, Función n variables, Fonction transcendante, Transcendental function, Función trascendente, Fonction variable complexe, Complex variable function, Función variable compleja, Nombre algébrique, Algebraic number, Número algebraico, Analyse diophantienne, Diophantine analysis, Critère transcendence, Transcendence criterion, Fonction arithmétique, Arithmetic function
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Institut de Mathématiques de Jussieu, Université P. et M. Curie (Paris VI), Théorie des Nombres Case 247, 175 rue du Chevaleret, 75013 Paris, France
ISSN:
0377-0427
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=15233707
Rights:
Copyright 2004 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.15233707
Database:
PASCAL Archive

Further Information

Given an analytic function of one complex variable f, we investigate the arithmetic nature of the values of f at algebraic points. A typical question is whether f(α) is a transcendental number for each algebraic number a. Since there exist transcendental entire functions f such that f(t)(α) ∈ Q[α] for any t ≥ 0 and any algebraic number a, one needs to restrict the situation by adding hypotheses, either on the functions, or on the points, or else on the set of values. Among the topics we discuss are recent results due to Andrea Surroca on the number of algebraic points where a transcendental analytic function takes algebraic values, new transcendence criteria by Daniel Delbos concerning entire functions of one or several complex variables, and Diophantine properties of special values of polylogarithms.