Note on Heath-Brown’s estimate for Heilbronn’s exponential sum
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- by Hong Bing Yu PDF
- Proc. Amer. Math. Soc. 127 (1999), 1995-1998 Request permission
Abstract:
We show that $S_h(a)=\sum ^p_{n=1}e(\frac {an^{hp}}{p^2})\ll (h,p-1)p^{11/12}$, which generalizes Heath-Brown’s estimate for Heilbronn’s exponential sum $S_1(a)$. We also give a simple proof of a crucial lemma in Heath-Brown’s work.References
- D. R. Heath-Brown, An estimate for Heilbronn’s exponential sum, Analytic number theory, Vol. 2 (Allerton Park, IL, 1995) Progr. Math., vol. 139, Birkhäuser Boston, Boston, MA, 1996, pp. 451–463. MR 1409372
- R. W. K. Odoni, Trigonometric sums of Heilbronn’s type, Math. Proc. Cambridge Philos. Soc. 98 (1985), no. 3, 389–396. MR 803598, DOI 10.1017/S0305004100063593
- S. A. Stepanov, The number of points of a hyperelliptic curve over a finite prime field, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 1171–1181 (Russian). MR 0252400
Additional Information
- Hong Bing Yu
- Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei 230026, Anhui, The People’s Republic of China
- Email: yuhb@ustc.edu.cn
- Received by editor(s): August 13, 1997
- Received by editor(s) in revised form: October 23, 1997
- Published electronically: March 17, 1999
- Additional Notes: Supported by the National Science Foundation of China
- Communicated by: David E. Rohrlich
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1995-1998
- MSC (1991): Primary 11L03
- DOI: https://doi.org/10.1090/S0002-9939-99-04776-0
- MathSciNet review: 1487349