Sum-product theorems and exponential sum bounds in residue classes for general modulus

Comptes Rendus Mathematique

Volumn 344, Issue 6, 2007, Pages 349-352

  Bourgain, Jean ^a  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

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Indexed keywords

EID: 33947221644     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2007.01.019     Document Type: Article

References (9)

1. Bourgain J. Mordell's exponential sum estimate revisited. JAMS 18 2 (2005) 477-499
2. *, q arbitrary. J. Analyse 97 (2005) 317-356
3. Bourgain J. Estimates on exponential sums related to the Diffie-Hellman distributions. GAFA 15 1 (2005) 1-34
4. *, where q is composite with few factors. GAFA 16 2 (2006) 327-366
5. p), Ann. of Math., in press
6. Bourgain J., Gamburd A., and Sarnak P. Sieving and expanders. C. R. Acad. Sci. Paris, Ser. I 343 3 (2006) 155-159
7. Bourgain J., Glibichuk A., and Konyagin S. Estimate for the number of sums and products and for exponential sums in fields of prime order. J. London Math. Soc. 73 (2006) 380-398
8. Bourgain J., Katz N., and Tao T. A sum-product estimate in finite fields and applications. GAFA 14 (2004) 27-57
9. Tao T., and Vu V. Additive Combinatorics. Cambridge Studies in Advanced Mathematics vol. 105 (2006), Cambridge University Press