Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order;Estimes sommes-produits et sur les sommes exponentielles associées à des sous-groupes d'un corps d'ordre premier

Comptes Rendus Mathematique

Volumn 337, Issue 2, 2003, Pages 75-80

  Bourgain, Jean ^a,b   Konyagin, S V ^c  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^c MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041704574     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1631-073X(03)00281-4     Document Type: Article

References (12)

1. J. Bourgain, N. Katz, T. Tao, A sum-product estimate in finite fields and their applications, ArXiv: math.CO/0301343v1, January 29, 2003, to appear in GAFA.
2. G.A. Edgar, C. Miller, Borel subrings of the reals, Proc. Amer. Math. Soc. 131 (2003) 1121-1129.
3. Gy. Elekes, On the umber of sums and products, Acta Arith. 81 (1997) 1121-1129.
4. P. Erdos, E. Szemerédi, On sums and the products of integers, in: P. Erdos, L. Alpár, G. Halász (Eds.), Studies in Pure Mathematics, Akadémiai Kiadó-Birkhäuser, Budapest-Basel, 1983, pp. 213-218 (To the memory of Paul Turan).
5. K. Ford, Sums and products from a finite set of real numbers, Ramanujan J. 2 (1998) 59-66.
6. D.R. Heath-Brown, S.V. Konyagin, New bounds for Gauss sums derived from k-th powers, and for Heilbronn's exponential sums, Quart. J. Math. 51 (2000) 221-235.
7. S.V. Konyagin, Estimates of trigonometric sums over subgroups and Gaussian sums, in: IV International Conference "Modern Problems of Number Theory and its Applications" dedicated to 180th anniversary of P.L. Chebyshev and 110th anniversary of I.M. Vinogradov, Topical Problems, Part 3, Department of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow, 2002, pp. 86-114 [in Russian].
8. N.M. Korobov, Exponential Sums and their Applications, Kluwer Academic, Dordrecht, 1992.
9. S.V. Konyagin, I.E. Shparlinski, Character Sums with Exponential Functions and their Applications, in: Cambridge Tracts in Math., Vol. 136, Cambridge University Press, Cambridge, 1999.
10. M. Nathanson, On sums and products of integers, Proc. Amer. Math. Soc. 125 (1997) 9-16.
11. I.E. Shparlinski, Estimates for Gauss sums, Math. Notes 50 (1991) 140-146.
12. J. Solymosi, On a question of Erdos and Szemerédi, Preprint, 2003.