Results 11 to 20 of about 164,093 (140)
A Kronecker-type identity and the representations of a number as a sum of three squares [PDF]
, 2017 By considering a limiting case of a Kronecker-type identity, we obtain an identity found by both Andrews and Crandall. We then use the Andrews-Crandall identity to give a new proof of a formula of Gauss for the representations of a number as a sum of ...
Mortenson, E.
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Eisenstein Series on Covers of Odd Orthogonal Groups [PDF]
, 2013 We study the Whittaker coefficients of the minimal parabolic Eisenstein series on the $n$-fold cover of the split odd orthogonal group $SO_{2r+1}$. If the degree of the cover is odd, then Beineke, Brubaker and Frechette have conjectured that the $p ...
Friedberg, Solomon, Zhang, Lei
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Identities on quadratic Gauss sums [PDF]
Transactions of the American Mathematical Society, 1990 Given a local field F F , each multiplicative character θ \theta of the split algebra F × F F \times F or of a separable quadratic extension of F F has an associated generalized Gauss sum γ θ F \gamma _\theta ^F .
Paul Gerardin, Wen-Ch' Ing Winnie Li
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Factorization of Numbers with the temporal Talbot effect: Optical implementation by a sequence of shaped ultrashort pulses [PDF]
, 2007 We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory.
Bertrand Girard +12 more
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A Note on the Classical Gauss Sums [PDF]
Mathematics, 2018 The main purpose of this paper is to study the computational problem of one kind rational polynomials of the classical Gauss sums, and using the purely algebraic methods and the properties of the character sums mod p (a prime with p ≡ 1 mod 12 ) to give an exact evaluation formula for it.
Tingting Wang, Guohui Chen
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The Entropy Sum of (A)dS Black Holes in Four and Higher Dimensions
, 2014 We present the "entropy sum" relation of (A)dS charged black holes in higher dimensional Einstein-Maxwell gravity, $f(R)$ gravity, Gauss-Bonnet gravity and gauged supergravity. For their "entropy sum" with the necessary effect of the un-physical "virtual"
Meng, Xin-he, Wang, Jia, Xu, Wei
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Finite Fields and Their Applications, 1998 Let \(m\) be an odd positive integer, \(n\) an arbitrary positive integer, and \(p\) a prime which does not divide \(m\). Let \(\mathbb{F}_{p}\) be a prime finite field, \(\mathbb{F}_{q}\) a finite extension of \(\mathbb{F}_{p}\) of degree \(f\), so \(q=p^{f}\), and \( \chi\) a multiplicative character of \(\mathbb{F}_{q}\) of order \(m\). If \( \zeta_{
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Factorization of numbers with Gauss sums: III. Algorithms with Entanglement
, 2012 We propose two algorithms to factor numbers using Gauss sums and entanglement: (i) in a Shor-like algorithm we encode the standard Gauss sum in one of two entangled states and (ii) in an interference algorithm we create a superposition of Gauss sums in ...
Schleich, W. P., Wölk, S.
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On Some Hypergeometric Summations [PDF]
, 2015 We develop a theoretical study of non-terminating hypergeometric summations with one free parameter. Composing various methods in complex and asymptotic analysis, geometry and arithmetic of certain transcendental curves and rational approximations of ...
Iwasaki, Katsunori
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DETERMINATIONS OF ANALOGUES OF GAUSS SUMS AND OTHER TRIGONOMETRIC SUMS [PDF]
International Journal of Number Theory, 2005 Explicit determinations of several classes of trigonometric sums are given. These sums can be viewed as analogues or generalizations of Gauss sums. In a previous paper, two of the present authors considered primarily sine sums associated with primitive odd characters.
Beck, Matthias +3 more
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