An explicit sum-product estimate in double-struck F signp

International Mathematics Research Notices

Volumn 2007, Issue , 2007, Pages

  Garaev, M Z ^a  

^a INSTITUTO DE MATEMÁTICAS   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 56749145306     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1093/imrn/rnm035     Document Type: Article

References (15)

1. Bourgain, J. "Estimates on exponential sums related to the Diffie-Hellman distributions." Geometric and Functional Analysis 15 (2005): 1-34.
2. Bourgain, J. "Mordell's exponential sum estimate revisited." Journal of the American Mathematical Society 18 (2005): 477-499.
3. Bourgain, J. "More on sum-product phenomenon in prime fields and its applications." International Journal of Number Theory 1 (2005): 1-32.
4. Bourgain, J., A. A. Glibichuk and S. V. Konyagin. "Estimates for the number of sums and products and for exponential sums in fields of prime order." Journal of the London Mathematical Society (2) 73 (2006): 380-398.
5. J. Bourgain, N. Katz and T. Tao. "A sum-product estimate in finite fields and their applications." Geometric and Functional Analysis 14 (2004): 27-57.
6. Chang, M.-C. "Some problems in combinatorial number theory," Preprint.
7. Erdös, P. and E. Szemerédi. "On sums and products of integers." Pp. 213-218 in Studies in pure mathematics, Basel: Birkh ? auser, 1983.
8. Glibichuk, A. A. "Combinatorial properties of sets of residues modulo a prime and the Erdös- Graham problem." Matematicheskie Zametki 79 (2006): 384-395; Mathematical Notes 79 (2006): 356-365.
9. Glibichuk, A. A. and S. V. Konyagin. "Additive properties of product sets in fields of prime order," Preprint.
10. Hart, D., A. Iosevich, and J. Solymosi. "Sum product estimates in finite fields via Kloosterman sums," Preprint.
11. Nathanson, M. B. Additive number theory. Inverse problems and the geometry of sumsets, 165. Springer-Verlag, New York, 1996.
12. Ruzsa, I. Z. "An application of graph theory to additive number theory." Scientia, Series A 3 (1989): 97-109.
13. Ruzsa, I. Z. "Sums of finite sets." Pp. 281-293 in Number Theory. NewYork: Springer, 1996.
14. Solymosi, J. "On the number of sums and products." Bulletin of the London Mathematical Society 37 (2005): 491-494.
15. Tao, T. and V. Vu. Additive combinatorics. Cambridge: Cambridge University Press, 2006.