On elliptic curves and random matrix theory

Mark Watkins[1]

  • [1] MAGMA Computer Algebra Group Department of Mathematics, Carslaw Building University of Sydney, Sydney, Australia

Journal de Théorie des Nombres de Bordeaux (2008)

  • Volume: 20, Issue: 3, page 829-845
  • ISSN: 1246-7405

Abstract

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Rubinstein has produced a substantial amount of data about the even parity quadratic twists of various elliptic curves, and compared the results to predictions from random matrix theory. We use the method of Heegner points to obtain a comparable (yet smaller) amount of data for the case of odd parity. We again see that at least one of the principal predictions of random matrix theory is well-evidenced by the data.

How to cite

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Watkins, Mark. "On elliptic curves and random matrix theory." Journal de Théorie des Nombres de Bordeaux 20.3 (2008): 829-845. <http://eudml.org/doc/10863>.

@article{Watkins2008,
abstract = {Rubinstein has produced a substantial amount of data about the even parity quadratic twists of various elliptic curves, and compared the results to predictions from random matrix theory. We use the method of Heegner points to obtain a comparable (yet smaller) amount of data for the case of odd parity. We again see that at least one of the principal predictions of random matrix theory is well-evidenced by the data.},
affiliation = {MAGMA Computer Algebra Group Department of Mathematics, Carslaw Building University of Sydney, Sydney, Australia},
author = {Watkins, Mark},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {method of Heegner points; predictions from random matrix theory; odd parity},
language = {eng},
number = {3},
pages = {829-845},
publisher = {Université Bordeaux 1},
title = {On elliptic curves and random matrix theory},
url = {http://eudml.org/doc/10863},
volume = {20},
year = {2008},
}

TY - JOUR
AU - Watkins, Mark
TI - On elliptic curves and random matrix theory
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2008
PB - Université Bordeaux 1
VL - 20
IS - 3
SP - 829
EP - 845
AB - Rubinstein has produced a substantial amount of data about the even parity quadratic twists of various elliptic curves, and compared the results to predictions from random matrix theory. We use the method of Heegner points to obtain a comparable (yet smaller) amount of data for the case of odd parity. We again see that at least one of the principal predictions of random matrix theory is well-evidenced by the data.
LA - eng
KW - method of Heegner points; predictions from random matrix theory; odd parity
UR - http://eudml.org/doc/10863
ER -

References

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