Results 11 to 20 of about 58,161 (160)
On quadratic Gauss sums and variations thereof
Cogent Mathematics, 2015 A number of new terminating series involving $\sin(n^2/k)$ and $\cos(n^2/k)$ are presented and connected to Gauss quadratic sums. Several new closed forms of generic Gauss quadratic sums are obtained and previously known results are generalized.
Milgram, Michael S., Glasser, Larry
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On the mean value of dedekind sum weighted by the quadratic gauss sum [PDF]
Czechoslovak Mathematical Journal, 2013 Let \(p\) be the prime greater than \(3\) and such that \(p\equiv 3 \mod 4\). The authors prove three identities. Among them the most important is \[ h_p^2=\frac {(p-1)(p-2)}6-\sum _{m=1}^{p-1}G(m^2-1,\chi _0;p)S(c^2,p), \] where \(h_p\), \(G(m,\chi ;q)\) and \(S(h,q)\) is the class number of the quadratic field \(\mathbb Q(\sqrt {-p})\), the quadratic
Wang, Tingting, Zhang, Wenpeng
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Equivariant Gauss sum of finite quadratic forms [PDF]
Forum Mathematicum, 2018 Abstract The classical quadratic Gauss sum can be thought of as an exponential sum attached to a quadratic form on a cyclic group. We introduce an equivariant version of Gauss sum for arbitrary finite quadratic forms, which is an exponential sum twisted by the action of the orthogonal group.
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On some conjectures on generalized quadratic Gauss sums and related problems
Finite Fields and Their Applications, 2023 The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic method and algebraic geometric methods. In this article, we prove two conjectures which were proposed in \cite{BLZ}.
Nilanjan Bag +2 more
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Moments of Generalized Quadratic Gauss Sums Weighted by L-Functions
Journal of Number Theory, 2002 The author studies moments of the generalized quadratic Gauss sum \[ G(n, \chi; q)=\sum_{a=1}^q\chi(a)\exp(2\pi ina^2/q),\;q,n\in\mathbb Z,\;q\geq 2, \] weighted by the Dirichlet \(L\)-function \(L(s, \chi)\), where \(\chi\) is the character modulo \(q\). Let \(p\) denote an odd prime and let \((n, p)=1\).
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Dynamic Transitions for Fast Joint Acquisition and Reconstruction of CEST- Rex$$ {R}_{ex} $$ and T1$$ {T}_1 $$. [PDF]
Magn Reson MedABSTRACT Purpose This work proposes a method for the simultaneous estimation of the exchange‐dependent relaxation rate Rex$$ {R}_{ex} $$ and the longitudinal relaxation time T1$$ {T}_1 $$ from a single acquisition. Methods A novel acquisition scheme was developed that combines CEST saturation with an inversion pulse and a Look‐Locker readout to capture
Huemer M +6 more
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The classification of 2-connected 7-manifolds [PDF]
, 2018 We present a classification theorem for closed smooth spin 2-connected 7-manifolds M. This builds on the almost-smooth classification from the first author's thesis.
Crowley, Diarmuid, Nordström, Johannes
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On the generalized quadratic Gauss sums and its upper bound estimate [PDF]
Journal of Mathematical Inequalities, 2021 Summary: The main purpose of this paper is to study generalized quadratic Gauss sums, then use the analytic methods, the properties of the classical Gauss sums and character sums to give a sharp upper bound estimate for it. In addition, we also give several interesting fourth and sixth power mean formulae for the sums.
Zhang, Jiafan, Lv, Xingxing
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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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On Tractable Exponential Sums [PDF]
, 2010 We consider the problem of evaluating certain exponential sums. These sums take the form $\sum_{x_1,...,x_n \in Z_N} e^{f(x_1,...,x_n) {2 \pi i / N}} $, where each x_i is summed over a ring Z_N, and f(x_1,...,x_n) is a multivariate polynomial with ...
A. Bulatov +10 more
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