Results 31 to 40 of about 164,472 (335)
A New Sum Analogous to Gauss Sums and Its Fourth Power Mean
The Scientific World Journal, 2014 The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind of new sum analogous to Gauss sums and give an interesting fourth power mean and a sharp upper bound estimate ...
Shaofeng Ru, Wenpeng Zhang
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IEEE Access, 2020 In multi-agent networked systems, parameter estimation problems arising in many practical applications are often required to solve Non-Linear Least Squares (NLLS) problems with the usual objective function (i.e., sum of squared residuals).
Mou Wu +3 more
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Gauss Sums and Binomial Coefficients
Journal of Number Theory, 2002 Let \(p= tn+r\) be a prime which splits in \(\mathbb{Q}(\sqrt{-t})\) where \(t\) has one of the following forms \[ \begin{aligned} t= k>3 &\;\text{ for a prime } k\equiv 3\pmod 4,\\ t= 4k &\;\text{ for a prime } k\equiv 1\pmod 4,\\ t= 8k &\;\text{ for an odd prime } k.
Lee, DH, Hahn, SG Hahn, Sang-Geun
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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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SECOND MOMENTS IN THE GENERALIZED GAUSS CIRCLE PROBLEM
Forum of Mathematics, Sigma, 2018 The generalized Gauss circle problem concerns the lattice point discrepancy of large spheres. We study the Dirichlet series associated to $P_{k}(n)^{2}$, where $P_{k}(n)$ is the discrepancy between the volume of the $k$-dimensional sphere of radius ...
THOMAS A. HULSE +3 more
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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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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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Summation identities for the Kummer confluent hypergeometric function 1F1(a; b;z)
Kuwait Journal of Science, 2023 The role which hypergeometric functions have in the numerical and symbolic calculation, especially in the fields of applied mathematics and mathematical physics motivated research in this paper.
Gradimir V. Milovanović +2 more
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Tokyo Journal of Mathematics, 2012 Let \(p > 2\) be a prime number, \(\mathbb F_p\) the prime finite field with \(p\) elements, \(\mathbb F^*_p\) its multiplicative cyclic group of order \(p-1\) and \(i = \sqrt{-1}\). The classical Gauss sum \(g_p\) is given by \[ \tau_p= \sum_{x \in \mathbb F^*_p} \left( \frac{x}{p} \right) e^{2 { \pi}i x/p}, \] where \( \left( \frac{x}{p} \right)\) is
GOMI, Yasushi +2 more
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On conformal field theories at fractional levels [PDF]
, 1998 For each lattice one can define a free boson theory propagating on the corresponding torus. We give an alternative definition where one employs any automorphism of the group $M^*/M$. This gives a wealth of conformal data, which we realize as some bosonic
Dixon +6 more
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