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Download e-book for kindle: Algorithmic Number Theory: 7th International Symposium, by Nigel Boston, Harris Nover (auth.), Florian Hess, Sebastian

By Nigel Boston, Harris Nover (auth.), Florian Hess, Sebastian Pauli, Michael Pohst (eds.)

ISBN-10: 3540360751

ISBN-13: 9783540360759

This publication constitutes the refereed complaints of the seventh overseas Algorithmic quantity concept Symposium, ANTS 2006, held in Berlin, Germany in July 2006.

The 37 revised complete papers provided including four invited papers have been conscientiously reviewed and chosen for inclusion within the booklet. The papers are geared up in topical sections on algebraic quantity concept, analytic and hassle-free quantity concept, lattices, curves and types over fields of attribute 0, curves over finite fields and functions, and discrete logarithms.

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Read or Download Algorithmic Number Theory: 7th International Symposium, ANTS-VII, Berlin, Germany, July 23-28, 2006. Proceedings PDF

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Additional info for Algorithmic Number Theory: 7th International Symposium, ANTS-VII, Berlin, Germany, July 23-28, 2006. Proceedings

Sample text

1. Overall distribution of ranks Table 2. Numbers of isogeny and isomorphism classes of curves range of N # isogeny classes # isomorphism classes 0-9999 10000-19999 20000-29999 30000-39999 40000-49999 50000-59999 60000-69999 70000-79999 80000-89999 90000-99999 100000-109999 110000-119999 120000-129999 38042 43175 44141 44324 44519 44301 44361 44449 44861 43651 44274 44071 44655 64687 67848 66995 66561 66275 65393 65209 64687 64864 63287 63410 63277 63467 0-129999 568824 845960 23 24 J. Cremona Table 3.

In the small number of cases where curves of rank greater than 1 have generators too large to be found easily by searching, we found the generator using 2-descent and in some cases 4-descent. The latter, for which algorithms were developed by Siksek and Womack, is now efficiently implemented in Magma. 5 Torsion Structures The distribution of the 15 possible structures for the torsion subgroups of the curves is given in Table 4. Here Cn denotes a cyclic group of order n. 6 Degrees of Modular Parametrizations As already mentioned, for most of the range the modular parametrization degrees were computed using a program of Mark Watkins (see [25] for the method).

C Springer-Verlag Berlin Heidelberg 2006 Cohen–Lenstra Heuristics of Quadratic Number Fields f (D) = (c0 + o(1)) 0<±D

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Algorithmic Number Theory: 7th International Symposium, ANTS-VII, Berlin, Germany, July 23-28, 2006. Proceedings by Nigel Boston, Harris Nover (auth.), Florian Hess, Sebastian Pauli, Michael Pohst (eds.)


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