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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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Density results for automorphic forms on Hilbert modular groups
, 2002 We give density results for automorphic representations of Hilbert modular groups. In particular, we show that there are infinitely many automorphic representations that have a prescribed discrete series factor at some (but not all) real places.Comment ...
Bruggeman, R. W. +2 more
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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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On Kloosterman sums connected with modular forms of half-itegral dimension [PDF]
, 1964 Marvin I. Knopp, John Smart
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Sign Changes of Kloosterman Sums with Almost Prime Moduli. II: Corrigendum [PDF]
, 2020 Ping Xi
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On the power mean of a sum analogous to the Kloosterman sum [PDF]
, 2017 Shane Chern
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Distress in parents of children with first-onset steroid-sensitive nephrotic syndrome. [PDF]
Pediatr Nephrol, 2023 Veltkamp F +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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