Sum-product theorem and exponential sum estimates in residue classes with modulus involving few prime factors;Un théorème somme-produit et des estimées des sommes exponentielles dans les classes de résidus avec module composé comportant un nombre borné de nombres premiers

Comptes Rendus Mathematique

Volumn 339, Issue 7, 2004, Pages 463-466

  Bourgain, Jean ^a   Chang, Mei Chu ^b  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 5044232224     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2004.08.007     Document Type: Article

References (8)

1. J. Bourgain, Mordell's exponential sum estimate revisited, preprint, 2004; JAMS, submitted for publication
2. J. Bourgain S. Konyagin Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order C. R. Acad. Sci. Paris, Ser. I 337 2 2003 75-80
3. J. Bourgain, A. Glibichuk, S. Konyagin, Estimate for the number of sums and products and for exponential sums in fields of prime order, J. London Math. Soc., submitted for publication
4. J. Bourgain N. Katz T. Tao A sum-product estimate in finite fields and their applications Geom. Funct. Anal. (GAFA) 14 1 2004 27-57
5. R. Heath-Brown An estimate for Heilbronn's exponential sum. In: Analytic Number Theory Proc. Conf. in honor of H. Halberstam 1996 Birkhäuser Boston, MA 451-463
6. R. Heath-Brown S. Konyagin New bounds for Gauss sums derived from kth powers, and for Heilbronn's exponential sums Quart. J. Math. 51 2000 221-235
7. S. Konyagin I. Shparlinski Character Sums with Exponential Functions and their Applications Cambridge Tracts in Mathematics vol. 136 1999 Cambridge University Press Cambridge
8. R. Odoni Trigonometric sums of Heilbronn's type Math. Proc. Comb. Philos. Soc. 98 1985 389-396