Some arithmetical applications of the sum-product theorems in finite fields

Lecture Notes in Mathematics

Volumn 1910, Issue , 2007, Pages 99-116

  Bourgain, J ^a  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

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EID: 34247595512     PISSN: 00758434     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-72053-9_6     Document Type: Conference Paper

References (15)

1. Bourgain, J.: Mordell's exponential sum estimate revisited. J. Amer. Math. Soc., 18, no. 2, 477-499 (2005)
2. Bourgain, J., Chang, M.: Exponential sum estimates over subgroups and almost subgroups of Z, where q is composite with few prime factors. Geom. Funct. Anal., submitted
3. Bourgain, J., Glivichuk, A., Konyagin, S.: Estimate for the number of sums and products and for exponential sums in fields of prime order. J. London Math. Soc., to appear
4. Bourgain, J., Katz, N., Tao, T.: A sum-product estimate in finite fields, and applications. Geom. Funct. Anal., 14, no. 2, 473-497 (2004)
5. Cochrane, T., Pinner, C.: An improved Mordell type bound for exponential sums. Amer. Math. Soc., 133, no. 2, 313-329, (2005)
6. Cochrane, T., Pinner, C., Rosenhouse, J.: Bounds on exponential sums and the polynomial Waring problem mod p. J. London Math. Soc. (2), 67, no. 2, 319-336 (2003)
7. kn modulo a prime. Integers, 4 (2004)
8. Heath-Brown, R.: An estimate for Heilbronn's exponential sum. Analytic Number Theory, Proc. Conf. in honor of H. Halberstam, Birkhäuser, Boston MA, 451-463 (1996)
9. Iwaniec, H., Kowalski, E.: Analytic Number Theory, American Mathematical Society, Colloquium Publications, 53, Providence (2004)
10. Konyagin, S.: Bounds on exponential sums over subgroups and Gauss sum. Proc. 4th Int. Conf. Modern Problems of Number Theory and its Applications, Moscow Lomonosov State Univ., Moscow, 86-114 (2002)
11. Konyagin, S., Shparlinski, I.: Character sums with exponential functions and their applications. Cambridge UP, Cambridge (1999)
12. Mordell, C.J.: On a sum analogous to a Gauss sum. Quart. J. Math., 3, 161-162 (1932)
13. Nathanson, M.: Additive Number Theory. Springer-Verlag, NY (1996)
14. Shparlinski, I.: On a question of Erdös and Graham. Arch. Math. (Basel), 78, no. 6, 445-448 (2002)
15. Tao, T., Vu, V.: Additive Combinatorics, to appear