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4 papers · 1 filter
A multimodular algorithm for computing Bernoulli numbers
David Harvey
We describe an algorithm for computing Bernoulli numbers. Using a parallel implementation, we have computed B(k) for k = 10^8, a new record. Our method is to compute B(k) modulo p…
Local-global principles for representations of quadratic forms
Jordan Ellenberg, Akshay Venkatesh
We prove the local-global principle holds for the problem of representations of quadratic forms by quadratic forms, in codimension . The proof uses the ergodic theory of $p…
A new upper bound for finite additive bases
Sinan Gunturk, Melvyn B. Nathanson
Let n(2,k) denote the largest integer n for which there exists a set A of k nonnegative integers such that the sumset 2A contains {0,1,2,...,n-1}. A classical problem in additive n…
Quasirandom Arithmetic Permutations
Joshua N. Cooper
Previously, the author introduced quasirandom permutations, permutations of which map intervals to sets with low discrepancy. Here we show that several natural numbe…