Topic
Kloosterman sum
About: Kloosterman sum is a research topic. Over the lifetime, 760 publications have been published within this topic receiving 11124 citations.
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Papers
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1 Jan 2002TL;DR: In this article, the spectral theorem for Harmonic analysis on the Euclidean plane and on the hyperbolic plane has been proved for Fuchsian groups on the Hyperbolic lattice point problems.
Abstract: Introduction Harmonic analysis on the Euclidean plane Harmonic analysis on the hyperbolic plane Fuchsian groups Automorphic forms The spectral theorem. Discrete part The automorphic Green function Analytic continuation of the Eisenstein series The spectral theorem. Continuous part Estimates for the Fourier coefficients of Maass forms Spectral theory of Kloosterman sums The trace formula The distribution of eigenvalues Hyperbolic lattice-point problems Spectral bounds for cusp forms Classical analysis Special functions References Subject index Notation index.
772 citations
TL;DR: The authors determine the weights of the orthogonals of some binary linear codes; the Melas code of length, the irreducible cyclic binary codes of length 2/sup t/+1, and the extended binary Goppa codes defined by polynomials of degree two.
Abstract: Starting from results on elliptic curves and Kloosterman sums over the finite field GE(2/sup t/), the authors determine the weights of the orthogonals of some binary linear codes; the Melas code of length, the irreducible cyclic binary code of length 2/sup t/+1, and the extended binary Goppa codes defined by polynomials of degree two. >
324 citations
TL;DR: The (weak) regularity of the new as well as of known monomial bent functions is discussed, the first example of a not weakly regular bent function is given and some criteria for an arbitrary quadratic function to be bent are proven.
Abstract: Considered are p-ary bent functions having the form f(x)=Tr/sub n/(/spl sigma//sub i=0//sup s/a/sub i/x/sup di/). A new class of ternary monomial regular bent function with the Dillon exponent is discovered. The existence of Dillon bent functions in the general case is an open problem of deciding whether a certain Kloosterman sum can take on the value -1. Also described is the general Gold-like form of a bent function that covers all the previously known monomial quadratic cases. The (weak) regularity of the new as well as of known monomial bent functions is discussed and the first example of a not weakly regular bent function is given. Finally, some criteria for an arbitrary quadratic function to be bent are proven.
242 citations
31 Jan 1988
230 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 9 |
| 2024 | 33 |
| 2023 | 34 |
| 2022 | 62 |
| 2021 | 33 |
| 2020 | 33 |