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ISSN 1088-6826(e) ISSN 0002-9939(p)

Polynomial Gauss sums

Author(s): Stephen D. Cohen; Michael Dewar; John B. Friedlander; Daniel Panario; Igor E. Shparlinski
Journal: Proc. Amer. Math. Soc. 133 (2005), 2225-2231.
MSC (2000): Primary 11L07, 11T23; Secondary 11B50, 11K31
Posted: March 17, 2005
MathSciNet review: 2138863
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Abstract | References | Similar articles | Additional information

Abstract: A recent bound for exponential sums by Friedlander, Hansen and Shparlinski is extended to twisted exponential sums with general polynomial arguments. As a by-product a new result about perfect powers in certain products of polynomials is established.

References:

1.: M. C. R. Butler, `The irreducible factors of over a finite field', J. London Math. Soc., 30 (1955), 480-482. MR 0071463 (17,130d)
2.: J. B. Friedlander, J. Hansen, and I. E. Shparlinski, `On character sums with exponential functions', Mathematika, 47 (2000), 75-85. MR 1924489 (2003g:11089)
3.: J. B. Friedlander, S. V. Konyagin and I. E. Shparlinski, `Some doubly exponential sums over $\mathbb{Z} _m$ ', Acta Arith., 105 (2002), 349-370. MR 1932568 (2004c:11147)
4.: W. C. W. Li, Number Theory with Applications, World Scientific Publishing Co., Singapore, 1996. MR 1390759 (98b:11001)
5.: R. Lidl and H. Niederreiter, Finite Fields, Cambridge University Press, Cambridge, 1997. MR 1429394 (97i:11115)

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Additional Information:

Stephen D. Cohen
Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, United Kingdom
Email: sdc@maths.gla.ac.uk

Michael Dewar
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
Email: mdewar@magma.ca

John B. Friedlander
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
Email: frdlndr@math.toronto.edu

Daniel Panario
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
Email: daniel@math.carleton.ca

Igor E. Shparlinski
Affiliation: Department of Computing, Macquarie University, Sydney, NSW 2109, Australia
Email: igor@ics.mq.edu.au

DOI: 10.1090/S0002-9939-05-08004-4
PII: S 0002-9939(05)08004-4
Received by editor(s): October 20, 2003
Posted: March 17, 2005
Additional Notes: The second author was supported in part by an NSERC Undergraduate Student Research Award
The third author was supported in part by NSERC grant A5123 and a Killam Research Fellowship.
The fourth author was supported in part by NSERC grant 238757
The fifth author was supported in part by ARC grant A69700294
Communicated by: Wen-Ching Winnie Li
Copyright of article: Copyright 2005, American Mathematical Society

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