Results 21 to 30 of about 78,424 (131)

Cancellations amongst Kloosterman sums [PDF]

Acta Arithmetica, 2016
We obtain several estimates for bilinear form with Kloosterman sums. Such results can be interpreted as a measure of cancellations amongst with parameters from short intervals. In particular, for certain ranges of parameters we improve some recent results of Blomer, Fouvry, Kowalski, Michel, and Milićević (2014) and Fouvry, Kowalski and Michel (2014).
Shparlinski, Igor E., Zhang, Tianping
openaire   +2 more sources

GENERALIZED KLOOSTERMAN SUMS AND THE FOURIER COEFFICIENTS OF CUSP FORMS.

, 1973
GENERALIZED KLOOSTERMAN SUMS AND THE FOURIER COEFFICIENTS OF CUSP ...
LOUISE ALAYNE STEPHENSON. PARSON (7982624)
core   +4 more sources

Kloosterman sums over finite Frobenius rings [PDF]

, 2019
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.Comment: 27 ...
Nica, Bogdan
core   +1 more source

On a Kind of Dirichlet Character Sums

Abstract and Applied Analysis, 2013
Let p≥3 be a prime and let χ denote the Dirichlet character modulo p.
Rong Ma, Yulong Zhang, Guohe Zhang
doaj   +1 more source

Some applications of smooth bilinear forms with Kloosterman sums [PDF]

, 2017
We revisit a recent bound of I. Shparlinski and T. Zhang on bilinear forms with Kloosterman sums, and prove an extension for correlation sums of Kloosterman sums against Fourier coefficients of modular forms.
Michel, Philippe, Philippe Michel, Étienne Fouvry, Milicevic, Djordje, Emmanuel Kowalski, Djordje Milićević, Blomer, V., Fouvry, Etienne, Valentin Blomer, Kowalski, Emmanuel, Blomer, Valentin, Kowalski, E., Sergeev, Armen, Fouvry, É., Milićević, D., Michel, P.   +15 more
core   +1 more source

On Sums of hyper-Kloosterman Sums [PDF]

, 2022
A formula of Kuznetsov allows one to interpret a smooth sum of Kloosterman sums as a sum over the spectrum of $GL(2)$ automorphic forms. In this paper, we construct a similar formula for the first hyper-Kloosterman sums using $GL(3)$ automorphic forms ...
Buttcane, Jack
core   +1 more source

Fourier expansions of complex-valued Eisenstein series on finite upper half planes

International Journal of Mathematics and Mathematical Sciences, 2006
We consider complex-valued modular forms on finite upper half planes Hq and obtain Fourier expansions of Eisenstein series invariant under the groups Γ=SL(2,Fp) and GL(2,Fp).
Anthony Shaheen, Audrey Terras
doaj   +1 more source

Power-moments of SL$_3(\mathbb Z)$ Kloosterman sums

, 1988
summary:Classical Kloosterman sums have a prominent role in the study of automorphic forms on GL$_2$ and further they have numerous applications in analytic number theory. In recent years, various problems in analytic theory of automorphic forms on GL$_3$
Djanković, Goran, Solomon Friedberg, Dorian Goldfeld, Daniel Bump   +3 more
core   +1 more source

On the Generalization of Lehmer Problem and High-Dimension Kloosterman Sums

The Scientific World Journal, 2014
For any fixed integer k≥2 and integer r with r, p=1, it is clear that there exist k integers 1≤ai≤p-1 i=1, 2, …, k such that a1a2⋯ak≡r mod p. Let N(k,r;p) denote the number of all a1, a2, ⋯ak such that a1a2⋯ak≡r mod p and 2†a1+a2+⋯ + ak.
Guohui Chen, Han Zhang
doaj   +1 more source

On some kloosterman sums

manuscripta mathematica, 1991
Let \({\mathbb{F}}_ q\) be the finite field with q elements, V be a finite- dimensional vector space over \({\mathbb{F}}_ q\), dim V\(=n\), \(L_ 1\), \(L_ 2\) linear forms and Q a quadratic form on V. The author proves an upper bound for the Kloosterman sum \[ K(L_ 1,L_ 2;Q):=\sum_{Q(v)\neq 0}\chi ((L_ 1(v)+L_ 2(v)(Q(v))^{-1}), \] where \(\chi\) is a ...
openaire   +1 more source