ON SOME EXPONENTIAL-SUMS OVER PRIME-NUMBE RS

Authors
Citation
E. Fouvry et P. Michel, ON SOME EXPONENTIAL-SUMS OVER PRIME-NUMBE RS, Annales Scientifiques de l'Ecole Normale Superieure, 31(1), 1998, pp. 93-130
Citations number
26
Categorie Soggetti
Mathematics,Mathematics
ISSN journal
00129593
Volume
31
Issue
1
Year of publication
1998
Pages
93 - 130
Database
ISI
SICI code
0012-9593(1998)31:1<93:OSEOPR>2.0.ZU;2-0
Abstract
Using methods inherited from algebraic geometry, we give bounds for ex ponential sums of the type Sigma(p less than or equal to x)(2 pi f(p)/ q), where q is a large prime number. f(X) is a general rational functi on over Z and the sum is performed over primes less than x(less than o r equal to q). Some extensions of the method are given when f(X) is of the form f(X) = X-k + uX (k integer different from 0 and 1). (C) Else vier, Paris.