|
Elementary estimates for a certain typeof Soto-Andrade sum
Author(s):
Imin
Chen
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1933-1939.
MSC (2000):
Primary 11L40;
Secondary 05C25, 20G40
Posted:
February 21, 2000
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
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.
References:
-
- 1.
- N. Celniker, S. Poulos, and A. Terras.
Is there life on finite upper half planes?
In A tribute to Emil Grosswald: Number Theory and Related Analysis, volume 143 of Contemporary Mathematics. AMS, 1993. MR 94h:05055 - 2.
- N. Katz.
Estimates for Soto-Andrade sums.
Journal für die Reine und Angewandte Mathematik, 438:143-161, 1993. MR 94h:11109 - 3.
- Wen-Ch'ing Winnie Li.
Number-theoretic constructions of ramanujan graphs.
Astérisque, 3-4(228):101-120, 1995. - 4.
- Wen-Ching Winnie Li.
Estimates of character sums arising from finite upper half planes.
In Cohen S. and Niederreiter H., editors, Finite fields and applications (Glasgow, 1995), number 233 in London Mathematical Society Lecture Notes. Cambridge University Press, 1996. - 5.
- Y. Sawabe.
Legendre character sums.
Hiroshima Mathematical Journal, 22:15-22, 1992. MR 93i:11147 - 6.
- J. Soto-Andrade.
Geometrical Gelfand models, tensor quotients, and Weil representations.
In Proceedings of Symposia in Pure Mathematics, volume 47, pages 305-316, 1987. - 7.
- A. Terras.
Are finite upper half plane graphs Ramanujan?
In Expanding Graphs (Princeton, NJ, 1992), volume 10 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 125-142. American Mathematical Society, Providence, RI, 1993. CMP 93:17 - 8.
- A. Weil.
On some exponential sums.
In Proceedings of the National Academy of Sciences, volume 34, pages 204-207, 1948.MR 10:234e
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
11L40,
05C25, 20G40
Retrieve articles in all Journals with MSC
(2000):
11L40,
05C25, 20G40
Additional Information:
Imin
Chen
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H3A 2K6
Email:
chen@math.mcgill.ca
DOI:
10.1090/S0002-9939-00-05591-X
PII:
S 0002-9939(00)05591-X
Received by editor(s):
September 8, 1998
Posted:
February 21, 2000
Additional Notes:
This research was supported by an NSERC postdoctoral fellowship and a grant from CICMA
Communicated by:
David E. Rohrlich
Copyright of article:
Copyright
2000,
American Mathematical Society
|
Comments: webmaster@ams.org