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Upper bounds on n-dimensional Kloosterman sums

✍ Scribed by Todd Cochrane; Ming-Chit Liu; Zhiyong Zheng

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 252 KB
Volume: 106
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2003.09.011

No coin nor oath required. For personal study only.

✦ Synopsis

Let p m be any prime power and K n ða; p m Þ be the Kloosterman sum

where the x i are restricted to values not divisible by p: Let m; n be positive integers with mX2 and suppose that p g jjðn þ 1Þ: We obtain the upper bound jK n ða; p m Þjpðn þ 1; p À 1Þp 1=2 minðg;mÀ2Þ p mn=2 ; for odd p: For p ¼ 2 we obtain the same bound, with an extra factor of 2 inserted.

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