Exponential sum estimates over subgroups and almost subgroups of ℤ*Q, where Q is composite with few prime factors

Geometric and Functional Analysis

Volumn 16, Issue 2, 2006, Pages 327-366

  Bourgain, J ^a   Chang, M C ^b  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Exponential sum; Sum and product set

Indexed keywords

EID: 33745439041     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-006-0558-7     Document Type: Article

References (19)

1. [B1] J. BOURGAIN, Estimates on exponential sums related to the Diffie-Hellman distributions, GAFA, Geom. fuct. anal. 15:1 (2005), 1-34.
2. [B2] J. BOURGAIN, Mordell's exponential sum estimate revisited, Journal of AMS 19:2 (2005), 477-499.
3. q, q arbitrary, J. Analysi, to appear.
4. [BC] J. BOURGAIN, M. CHANG, Sum-product theorem and exponential sum estimates in residue classes with moduli involving few prime factors, preprint (2004).
5. [BK] 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 337:2 (2003), 75-80.
6. [BGK] J. BOURGAIN, A. GLIBICHUK, S. KONYAGIN, Estimate for the number of sums and products and for exponential sums in fields of prime order, submitted to J. London MS.
7. [BKT] J. BOURGAIN, N. KATZ, T. TAO, A sum-product estimate in finite fields and their applications, GAFA, Geom. funct. anal. 14:1 (2004), 27-57.
8. [ES] P. ERDOS, E. SZEMERÉDI, On sums and products of integers, in "Studies in Pure Mathematics; to the memory of P. Turán " (P. Erdös, L. Alpár, G. Halász, eds.) (1983), 213-218.
9. [HR] H. HALBERSTAM, H.-E. RICHERT, Sieve Methods. London Math. Soc. Monographs 4, Academic Press (1974).
10. [HRo] H. HALBERSTAM, K. ROTH, Sequences, vol. 1, Oxford Press, 1966.
11. [He] R. HEATH-BROWN, An estimate for Heilbronn's exponential sum, Analytic Number Theory, Proc. Conf. in honor of H. Halberstam, Birkhäuser, Boston MA (1996), 451-463.
12. th powers, and for Heilbronn's exponential sums, Quat. J. Math. 51 (2000), 221-235.
13. [KS] S. KONYAGIN, I. SHPARLINSKI, Character Sums with Exponential Functions and their Applications, Cambridge Tracts in Mathematics, 136, Cambridge UP, Cambridge (1999).
14. [LR] LACZKOVICH, I. RUZSA, The number of homothetic subsets, in 'The Mathemattics of P. Erdos, II. (R.L. Graham, J. Nesetril, eds.), Springer, Algorithms Combin. 14 (1997), 294-302.
15. [M] L.J. MORDELL, On a sum analogous to a Gauss sum, Quart. J. Math 3 (1932), 161-162.
16. [N] M.B. NATHANSON, Additive Number Theory: Inverse Problems and the Geometry of Sumsets, Springer, 1996.
17. [O] R. ODONI, Trigonometric sums of Heilbronn's type, Math. Proc. Comb. Phil. Soc. 98 (1985), 389-396.
18. [S] J. SOLYMOSI, On the number of sums and products, preprint (2003).
19. [TV] T. TAO, V. VU, Additive combinatorics preprint.