Refined upper bounds for the linear Diophantine problem of Frobenius
Matthias Beck, Shelemyahu Zacks
Abstract
We study the Frobenius problem: given relatively prime positive integers a1,...,ad, find the largest value of t (the Frobenius number g(a1,...,ad)) such that m1 a1 + ... md ad = t has no solution in nonnegative integers m1,...,md. We introduce a method to compute upper bounds for g(a1,a2,a3), which seem to grow considerably slower than previously known bounds. Our computations are based on a formula for the restricted partition function, which involves Dedekind-Rademacher sums, and the reciprocity law for these sums.
Create a lesson
Related papers
Rational points on loxodromic K3 surfaces and complex dynamics
Damián Gvirtz-Chen, Zhizhong Huang, Zhuchao Ji et al.
Ramanujan-type congruences for the smallest parts function
Larry Rolen
Some instances of modularity for residually reducible representations in the mixed case
Luis V. Dieulefait
Classification of torsion of elliptic curves over sextic fields
Filip Najman
A generalization of the Dirichlet approximation theorem for affine actions on the real line
Mohammad Javaheri
On ill-distributed B3 and B4 sets
André Hisatsuga, Rafael Miyazaki, Cosmin Pohoata