New bounds for Gauss sums derived from kth powers, and for Heilbronn's exponential sum

Quarterly Journal of Mathematics

Volumn 51, Issue 2, 2000, Pages 221-235

  Heath Brown, D R ^a   Konyagin, S ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034404750     PISSN: 00335606     EISSN: None     Source Type: Journal    
DOI: 10.1093/qjmath/51.2.221     Document Type: Article

References (8)

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2. D. R. Heath-Brown, An estimate for Heilbronn's exponential sum, Analytic number theory: Proceedings of a conference in honor of Heini Halberstam, Birkhäuser, Boston, MA, (1996), 451-463.
3. S. V. Konyagin, On estimates of Gaussian sums and Waring's problem for a prime modulus, Proc. Steklov Inst. Math. 198 (1994), 105-117.
4. D. A. Mit'kin, An estimate for the number of roots of some comparisons by the Stepanov method, Mater. Zametki 51 (1992), 52-58, (Translated as Math. Notes 51 (1992), 565-570.)
5. D. A. Mit'kin, An estimate for the number of roots of some comparisons by the Stepanov method, Mater. Zametki 51 (1992), 52-58, (Translated as Math. Notes 51 (1992), 565-570.)
6. H. L. Montgomery, R. C. Vaughan, and T. D. Wooley, Some remarks on Gauss sums associated with kth powers, Math. Proc. Camb. Phil. Soc. 118 (1995), 21-33.
7. I. E. Shparlinski, On Bounds of Gaussian Sums, Mater. Zametki 50 (1991), 122-130.
8. S. A. Stepanov, The number of points of a hyperelliptic curve over a prime field, Izv. Akad. Nauk SSSR Ser. Mater. 33 (1969), 1171-1181.