Semi-analytical approximation of the normal derivative of the heat simple layer potential near the boundary of a two-dimensional domain [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. ИнформатикаA semi-analytical approximation of the normal derivative of the simple layer heat potential near the boundary of a two-dimensional domain with $C^{5} $ smoothness is proposed.
Ivanov, Dmitrii Yurievich
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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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Factorization of numbers with Gauss sums: I. Mathematical background
, 2011 We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples.
Averbukh, I. Sh. +4 more
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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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On the Dedekind Sums and the Quadratic Gauss Sums FULL TEXT
, 2012 Tingting Wang, Wenpeng Zhang
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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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Lattices with many Borcherds products [PDF]
, 2015 We prove that there are only finitely many isometry classes of even lattices $L$ of signature $(2,n)$ for which the space of cusp forms of weight $1+n/2$ for the Weil representation of the discriminant group of $L$ is trivial.
Bruinier, Jan Hendrik +2 more
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The value distribution of incomplete Gauss sums
, 2012 It is well known that the classical Gauss sum, normalized by the square-root number of terms, takes only finitely many values. If one restricts the range of summation to a subinterval, a much richer structure emerges.
Chinen +4 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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