10 citations · 24 across the 11 of their papers we have counts for
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Determinations of Analogues of Gauss Sums and Other Trigonometric Sums
Matthias Beck, Bruce C. Berndt, O-Yeat Chan +1
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…
Higher-dimensional Dedekind sums and their bounds arising from the discrete diagonal of the n-cube
Matthias Beck, Sinai Robins, Shelemyahu Zacks
Higher-dimensional Dedekind sums are defined as a generalization of a recent 1-dimensional probability model of Dilcher and Girstmair to a d-dimensional cube. The analysis of the f…
The Reciprocity Law for Dedekind Sums via the constant Ehrhart coefficient
Matthias Beck
We obtain a new motivated proof of the reciprocity law for Dedekind sums by computing the constant coefficient of the Ehrhart polynomial for a rectangular triangle in two ways. On…
Refined upper bounds for the linear Diophantine problem of Frobenius
Matthias Beck, Shelemyahu Zacks
We study the Frobenius problem: given relatively prime positive integers a_1,...,a_d, find the largest value of t (the Frobenius number g(a_1,...,a_d)) such that m_1 a_1 + ... m_d…
An extension of the Frobenius coin-exchange problem
Matthias Beck, Sinai Robins
Given positive integers with , we call an integer t representable if there exist nonnegative integers such that $t = m_1 a_1 + ..…
Some experimental results on the Frobenius problem
Matthias Beck, David Einstein, Shelemyahu Zacks
We study the Frobenius problem: given relatively prime positive integers , find the largest value of t (the Frobenius number) such that has…