Congruent number theta coefficients to 1012

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Abstract

We report on a computation of congruent numbers, which subject to the Birch and Swinnerton-Dyer conjecture is an accurate list up to 1012. The computation involves multiplying long theta series as per Tunnell (1983). The method, which we describe in some detail, uses a multimodular disk based technique for multiplying polynomials out-of-core which minimises expensive disk access by keeping data truncated. © 2010 Springer-Verlag Berlin Heidelberg.

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Hart, W. B., Tornaría, G., & Watkins, M. (2010). Congruent number theta coefficients to 1012. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6197 LNCS, pp. 186–200). https://doi.org/10.1007/978-3-642-14518-6_17

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