Displaying similar documents to “Note on the quadratic Gauss sums.”

Renormalization of exponential sums and matrix cocycles

Alexander Fedotov, Frédéric Klopp (2004-2005)

Séminaire Équations aux dérivées partielles

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In this paper, we present a new point of view on the renormalization of some exponential sums stemming from number theory. We generalize this renormalization procedure to study some matrix cocycles arising in spectral problems of quantum mechanics

Half Gauss Sums.

Bruce C. Berndt, Ronald J. Evans (1980)

Mathematische Annalen

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Equality of Dedekind sums modulo 8ℤ

Emmanuel Tsukerman (2015)

Acta Arithmetica

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Using a generalization due to Lerch [Bull. Int. Acad. François Joseph 3 (1896)] of a classical lemma of Zolotarev, employed in Zolotarev's proof of the law of quadratic reciprocity, we determine necessary and sufficient conditions for the difference of two Dedekind sums to be in 8ℤ. These yield new necessary conditions for equality of two Dedekind sums. In addition, we resolve a conjecture of Girstmair [arXiv:1501.00655].

The hybrid power mean of quartic Gauss sums and Kloosterman sums

Li Xiaoxue, Hu Jiayuan (2017)

Open Mathematics

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The main purpose of this paper is using the analytic method and the properties of the classical Gauss sums to study the computational problem of one kind fourth hybrid power mean of the quartic Gauss sums and Kloosterman sums, and give an exact computational formula for it.

On quadratic Hurwitz forms. I

Jiří Gregor (1981)

Aplikace matematiky

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Homogeneous quadratic polynomials f in n complex variables are investigated and various necessary and sufficient conditions are given for f to be nonzero in the set Γ ( n ) = z ∈ C ( n ) : R e z > 0 . Conclusions for the theory of multivariable positive real functions are formulated with applications in multivariable electrical network theory.