Higher dimensional Dedekind sums in function fields
Abdelmejid Bayad, Yoshinori Hamahata (2012)
Acta Arithmetica
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Displaying similar documents to “Binary Kloosterman sums using Stickelberger's theorem and the Gross-Koblitz formula”
Higher dimensional Dedekind sums in function fields
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Zhi-Wei Sun (2001)
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On the hybrid mean value of Cochrane sums and generalized Kloosterman sums
Tingting Wang (2012)
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Powers of 2 with five distinct summands
Vsevolod F. Lev (2008)
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Waring's problem for fields
William Ellison (2013)
Acta Arithmetica
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If K is a field, denote by P(K,k) the a ∈ K which are sums of kth powers of elements of K, by P⁺(K,k) the set of a ∈ K which are sums of kth powers of totally positive elements of K. We give some simple conditions for which there exist integers w(K,k) and g(K,k) such that: a ∈ P(K,k) implies that a is the sum of at most w(K,k) kth powers; a ∈ P⁺(K,k) implies that a is the sum of at most g(K,k) totally positive kth powers. We apply the results to characterise functions that are sums of...
Fourth power mean of character sums
Zhefeng Xu, Wenpeng Zhang (2008)
Acta Arithmetica
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On Some Sets Of Integers With Equal Sums Of Like Powers
Alfred Moessner, George Xeroudakes (1954)
Publications de l'Institut Mathématique
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Unification of zero-sum problems, subset sums and covers of .
Sun, Zhiwei (2003)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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A reciprocity theorem and a three-term relation for generalized Dedekind-Rademacher sums
L. Carlitz (1980)
Acta Arithmetica
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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.
Hybrid mean value for a generalization of a problem of D. H. Lehmer
Huaning Liu, Wenpeng Zhang (2007)
Acta Arithmetica
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Slim exceptional sets for sums of fourth and fifth powers
Koichi Kawada, Trevor D. Wooley (2002)
Acta Arithmetica
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A mean value related to the D. H. Lehmer problem and Kloosterman sums
Wenpeng Zhang, Zhaoxia Wu (2010)
Acta Arithmetica
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Negative values of cosine sums
Imre Z. Ruzsa (2004)
Acta Arithmetica
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Generalizations of Dedekind sums and their reciprocity laws
Yumiko Nagasaka, Kaori Ota, Chizuru Sekine (2003)
Acta Arithmetica
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The hybrid mean value of Dedekind sums and two-term exponential sums
Chang Leran, Li Xiaoxue (2016)
Open Mathematics
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In this paper, we use the mean value theorem of Dirichlet L-functions, the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the two-term exponential sums, and give an interesting identity and asymptotic formula for it.
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].