Effective limit distribution of the Frobenius numbers
2014 ◽
Vol 151
(5)
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pp. 898-916
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The Frobenius number$F(\boldsymbol{a})$of a lattice point$\boldsymbol{a}$in$\mathbb{R}^{d}$with positive coprime coordinates, is the largest integer which cannotbe expressed as a non-negative integer linear combination of the coordinates of$\boldsymbol{a}$. Marklof in [The asymptotic distribution of Frobenius numbers, Invent. Math.181(2010), 179–207] proved the existence of the limit distribution of the Frobenius numbers, when$\boldsymbol{a}$is taken to be random in an enlarging domain in$\mathbb{R}^{d}$. We will show that if the domain has piecewise smooth boundary, the error term for the convergence of the distribution function is at most a polynomial in the enlarging factor.
Estimating the cumulative distribution function for the linear combination of gamma random variables
2017 ◽
Vol 20
(5)
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pp. 939-951
1982 ◽
Vol 37
(1)
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pp. 168-169
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Keyword(s):
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1998 ◽
Vol 18
(5)
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pp. 1049-1073
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Keyword(s):
2019 ◽
Vol 158
(1)
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pp. 216-234
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Keyword(s):
Keyword(s):