Results 31 to 40 of about 7,921 (138)

On Sums of SL(3,Z) Kloosterman Sums

, 2012
We show that sums of the SL(3,Z) long element Kloosterman sum against a smooth weight function have cancellation due to the variation in argument of the Kloosterman sums, when each modulus is at least the square root of the other.
Buttcane, Jack
core  

Kloosterman sums with multiplicative coefficients [PDF]

Izvestiya: Mathematics, 2018
The series of some new estimates for the sums of the type \[ S_{q}(x;f)\,=\,\mathop{{\sum}'}\limits_{n\leqslant x}f(n)e_{q}(an^{*}+bn) \] is obtained. Here $q$ is a sufficiently large integer, $\sqrt{q}(\log{q})\!\ll\!x\leqslant q$, $a,b$ are integers, $(a,q)=1$, $e_{q}(v) = e^{2 iv/q}$, $f(n)$ is a multiplicative function, $nn^{*}\equiv 1 \pmod{q ...
openaire   +3 more sources

The Exotic Inverted Kloosterman Sum

International Mathematics Research Notices
Abstract Let $B$ be a product of finitely many finite fields containing $\mathbb{F}_{q}$, $\psi :\mathbb{F}_{q}\to \overline{\mathbb{Q}}_\ell ^{*}$ a nontrivial additive character, and $\chi : B^{*}\to \overline{\mathbb{Q}}_\ell ^{*}$ a multiplicative character.
Fu, Lei, Wan, Daqing
openaire   +3 more sources

On s-dimensional incomplete Kloosterman sums

Journal of Number Theory, 2010
Let \[ K_{s}(\vec{a},\vec{M},\vec{N};p)=\sum\limits_{n_{1}=M_{1}+1}^{M_{1}+N_{1}}\cdots\sum\limits_{n_{s}=M_{s}+1}^{M_{s}+N_{s}}e_{p}(a_{1}n_{1}+\cdots+a_{s}n_{s}+a_{s+1}\overline{n_{1}\cdots n_{s}}), \] where \(\vec{a}=(a_{1},\dots,a_{s+1})\in\mathbb{Z}^{s+1}\), \(\vec{M}=(M_{1},\dots,M_{s})\in\mathbb{Z}^{s}\), \(\vec{N}=(N_{1},\dots,N_{s})\in\mathbb ...
Wang, Yunjie, Li, Hongze
openaire   +2 more sources

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.
openaire   +2 more sources

The Lifting of Kloosterman Sums

Journal of Number Theory, 1995
To prove the relative trace formula for \(\text{GL}(2)\) [see \textit{H. Jacquet} and the author, Bull. Soc. Math. Fr. 120, 263-295 (1992; Zbl 0785.11032), the author, J. Reine Angew. Math. 400, 57-121 (1989; Zbl 0665.10020)]\ Jacquet and the author have shown that there are certain identities for local Kloosterman sums. On basis of those local results
openaire   +2 more sources

Parametrization of Kloosterman sets and $\mathrm{SL}_3$-Kloosterman sums

, 2020
39 ...
Kıral, Eren Mehmet, Nakasuji, Maki
openaire   +3 more sources

Bounds for Incomplete Hyper-Kloosterman Sums

Journal of Number Theory, 1999
For a prime \(p \geq 3\), the ``complete'' hyper-Kloosterman sum is \[ Kl _m(p)=\sum_{d_1=1}^{p-1}\cdots \sum_{d_m=1}^{p-1}e\left (\frac{d_1+\dotsb +d_m+\overline{d_1\dotsb d_m}}{p}\right), \] where the bar indicates multiplicative inverse \(\pmod{p}\).
openaire   +1 more source

Kuznetsov Formulas for Generalized Kloosterman Sums

Rocky Mountain Journal of Mathematics, 1997
The Kuznetsov trace formula [\textit{N. V. Kuznetsov}, Mat. Sb., Nov. Ser. 111(153), 334-383 (1980; Zbl 0427.10016)] relates a weighted sum of classical Kloosterman sums to a weighted sum of Fourier coefficients of \(GL(2)\) automorphic forms and other spectral information.
openaire   +3 more sources

Exponential Function Analogue of Kloosterman Sums

Rocky Mountain Journal of Mathematics, 2004
Let \(p\) be a prime, and let \(t\) be a divisor of \(p-1\). Further let \(\mathbb{Z}^*_t\) be the subset of \(\{0,\dots, t-1\}\) consisting of \(\varphi(t)\) invertible elements, where \(\varphi(t)\) is the Euler function. For any integers \(a\) and \(b\) with \(0\leq a\), \(b\leq p-1\), let \(K_g(a,b)= \sum_{x\in\mathbb{Z}^*_t} e(ag^x+ bg^{x^{-1}})\),
openaire   +2 more sources