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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Note on Heath-Brown's estimate
for Heilbronn's exponential sum


Author: Hong Bing Yu
Journal: Proc. Amer. Math. Soc. 127 (1999), 1995-1998
MSC (1991): Primary 11L03
Published electronically: March 17, 1999
MathSciNet review: 1487349
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Abstract | References | Similar Articles | Additional Information

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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04776-0
PII: S 0002-9939(99)04776-0
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
Article copyright: © Copyright 1999 American Mathematical Society