We prove that to find a nontrivial integer linear relation between vectors of a lattice L IRn , whose euclidean length is at most M, one needs O n5+ (ln Mn/)1+ binary operations f...
In this note we address the question whether for a given prime number p, the zeta-function of a number field always determines the p-part of its class number. The answer is known t...
In 1986, following the work of Schoof on counting points on elliptic curves over finite fields, new algorithms for primality proving emerged, due to Goldwasser and Kilian on the on...
We describe two techniques for fast multiple-precision evaluation of linearly convergent series, including power series and Ramanujan series. The computation time for N bits is O(...
Call a set of integers {b1, b2, . . . , bk} admissible if for any prime p, at least one congruence class modulo p does not contain any of the bi. Let (x) be the size of the largest...