Kloosterman sums and finite field extensions
L. Carlitz (1969)
Acta Arithmetica
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Displaying similar documents to “On the order of ”
Kloosterman sums and finite field extensions
On Waldspurger's theorem
Henryk Iwaniec (1987)
Acta Arithmetica
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A reciprocity congruence for an analogue of the Dedekind sum and quadratic reciprocity
Jeffrey L. Meyer (2000)
Journal de théorie des nombres de Bordeaux
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In the transformation formulas for the logarithms of the classical theta-functions, certain sums arise that are analogous to the Dedekind sums in the transformation of the logarithm of the eta-function. A new reciprocity law is established for one of these analogous sums and then applied to prove the law of quadratic reciprocity.
Sums of coefficients of Hecke series
Aleksandar Ivić, Tom Meurman (1994)
Acta Arithmetica
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Exponential sums and additive problems involving square-free numbers
Jörg Brüdern, Alberto Perelli (1999)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Low lying zeros of families of -functions
H. Luo Iwaniec, P. Sarnak (2000)
Publications Mathématiques de l'IHÉS
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On the sphere problem.
Fernando Chamizo, Henryk Iwaniec (1995)
Revista Matemática Iberoamericana
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One of the oldest problems in analytic number theory consists of counting points with integer coordinates in the d-dimensional ball. It is very easy to find a main term for the counting function, but the size of the error term is difficult to estimate (...).
Weyl sums and atomic energy oscillations.
Antonio Córdoba, Charles L. Fefferman, Luis A. Seco (1995)
Revista Matemática Iberoamericana
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We extend Van der Corput's method for exponential sums to study an oscillating term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations.