Results 41 to 50 of about 3,574 (134)
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 ...
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The Exotic Inverted Kloosterman Sum
International Mathematics Research NoticesAbstract 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
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Generalized Dedekind sums and equidistribution mod 1
, 2015 Dedekind sums are well-studied arithmetic sums, with values uniformly distributed on the unit interval. Based on their relation to certain modular forms, Dedekind sums may be defined as functions on the cusp set of $SL(2,\mathbb{Z})$.
Burrin, Claire
core
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
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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.
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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
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Parametrization of Kloosterman sets and $\mathrm{SL}_3$-Kloosterman sums
, 2020 39 ...
Kıral, Eren Mehmet, Nakasuji, Maki
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Uncovering spatial representations from spatiotemporal patterns of rodent hippocampal field potentials. [PDF]
Cell Rep Methods, 2021 Cao L, Varga V, Chen ZS.
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Awake Hippocampal-Cortical Co-reactivation Is Associated with Forgetting. [PDF]
J Cogn Neurosci, 2023 Tanrıverdi B +6 more
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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 \(\pmod{p}\).
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