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Elementary estimates for a certain typeof Soto-Andrade sum

Author: Imin Chen
Journal: Proc. Amer. Math. Soc. 128 (2000), 1933-1939
MSC (2000): Primary 11L40; Secondary 05C25, 20G40
Published electronically: February 21, 2000
MathSciNet review: 1707143
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Abstract | References | Similar Articles | Additional Information


This paper shows that a certain type of Soto-Andrade sum can be estimated in an elementary way which does not use the Riemann hypothesis for curves over finite fields and which slightly sharpens previous estimates for this type of Soto-Andrade sum. As an application, we discuss how this implies that certain graphs arising from finite upper half planes in odd characteristic are Ramanujan without using the Riemann hypothesis.

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Additional Information

Imin Chen
Affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H3A 2K6

Received by editor(s): September 8, 1998
Published electronically: February 21, 2000
Additional Notes: This research was supported by an NSERC postdoctoral fellowship and a grant from CICMA
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2000 American Mathematical Society

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