A new upper bound is obtained for the incomplete hyper-Kloosterman sum by means of Burgess' estimate, provided the number of variables in the sum is sufficiently large. ## 1999 Academic Press In connection with the problem of expressing integers by a positive definite integral quadratic form in fo
Bounds of incomplete multiple Kloosterman sums
β Scribed by Igor E. Shparlinski
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 108 KB
- Volume
- 126
- Category
- Article
- ISSN
- 0022-314X
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β¦ Synopsis
We obtain an estimate for incomplete multiple Kloosterman sums modulo a prime which improves the previous result of W. Luo.
π SIMILAR VOLUMES
Let p m be any prime power and K n Γ°a; p m Γ 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 jjΓ°n ΓΎ 1Γ: We obtain the upper bound jK n Γ°a; p m ΓjpΓ°n ΓΎ 1; p Γ 1Γp 1=2 minΓ°g;mΓ2Γ p mn=2 ; for odd p: For p ΒΌ
The purpose of this article is to prove several identities of Kloosterman sums based on the recent progress in the theory of relative trace formulas. (f) 1995 Academic Press. Inc.
An upper bound for the extended Kloosterman sum over Galois rings is derived. This bound is then used to construct new sequence families with low correlation properties and alphabet size a power of a prime.
Improved lower bounds on multiple distinct sums sets are given. Lower bounds for the more general case of multiple difference set of a distinct sum set are considered.