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Kloosterman sums on orthogonal groups
The Ramanujan JournalWe study Kloosterman sums on the orthogonal groups $SO_{3,3}$ and $SO_{4,2}$, associated to short elements of their respective Weyl groups. An explicit description for these sums is obtained in terms of multi-dimensional exponential sums.
Mujdei, Catinca
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On Certain Values of Kloosterman Sums [PDF]
IEEE Transactions on Information Theory, 2009 Let $K_{q^n}(a)$ be a Kloosterman sum over the finite field $\F_{q^n}$ of characteristic $p$. In this note so called subfield conjecture is proved in case $p>3$: if $a\ne0$ belongs to the proper subfield $\F_q$ of $\F_{q^n}$, then $K_{q^n}(a)\ne-1$. This completes recent works on the subfield conjecture by Shparlinski, and Moisio and Lisonek.
Väänänen Keijo +2 more
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On sums of hyper-Kloosterman sums
Forum Mathematicum, 2023 Abstract A formula of Kuznetsov allows one to interpret a smooth sum of Kloosterman sums as a sum over the spectrum of GL
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Kloosterman sums over finite Frobenius rings
, 2021 We study Kloosterman sums in a generalized ring-theoretic context, that of finite commutative Frobenius rings. We prove a number of identities for twisted Kloosterman sums, loosely clustered around moment computations.
Nica, Bogdan, Bogdan Nica
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An Algorithm for the explicit evaluation of GL(n, R) Kolsterman sums [PDF]
, 2009 An algorithm for the explicit evaluation of Kloosterman sums for GL(n, R) for n ≥2 and an implementation in the Mathematics package GL(n) pack are ...
Broughan, Kevin A.
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Symplectic Kloosterman Sums and Poincar\'e Series [PDF]
, 2021 We prove power-saving bounds for general Kloosterman sums on $\operatorname{Sp}(4)$ associated to all Weyl elements via a stratification argument coupled with $p$-adic stationary phase methods. We relate these Kloosterman sums to the Fourier coefficients
Man, Siu Hang, Siu Hang Man
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Double sums of Kloosterman sums in finite fields [PDF]
Finite Fields and Their Applications, 2019 We bound double sums of Kloosterman sums over a finite field ${\mathbb F}_{q}$, with one or both parameters ranging over an affine space over its prime subfield ${\mathbb F}_p \subseteq {\mathbb F}_{q} $. These are finite fields analogues of a series of recent results by various authors in finite fields and residue rings.
Simon Macourt, Igor E. Shparlinski
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Kloosterman sums in residue classes [PDF]
, 2015 We prove upper bounds for sums of Kloosterman sums against general arithmetic weight functions. In particular, we obtain power cancellation in sums of Kloosterman sums over arithmetic progressions, which is of square-root strength in any xed primitive ...
Milicevic, D. +3 more
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A note on the mean value of the general Kloosterman sums [PDF]
, 2011 summary:The main purpose of this paper is to use the analytic method to study the calculating problem of the general Kloosterman sums, and give an exact calculating formula for ...
Yao, Weili
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Kloosterman sums do not correlate with periodic functions
, 2023 We provide uniform bounds for sums of Kloosterman sums in all arithmetic progressions. As a consequence, we find that Kloosterman sums do not correlate with periodic functions.Comment: 24 ...
Steiner, Raphael S.
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