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| Product Code: | CONM/463 |
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| eBook ISBN: | 978-0-8218-8142-2 |
| Product Code: | CONM/463.E |
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| Softcover ISBN: | 978-0-8218-4320-8 |
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| Softcover ISBN: | 978-0-8218-4320-8 |
| Product Code: | CONM/463 |
| List Price: | $130.00 |
| MAA Member Price: | $117.00 |
| AMS Member Price: | $104.00 |
| eBook ISBN: | 978-0-8218-8142-2 |
| Product Code: | CONM/463.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| Softcover ISBN: | 978-0-8218-4320-8 |
| eBook ISBN: | 978-0-8218-8142-2 |
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Book DetailsContemporary MathematicsVolume: 463; 2008; 129 ppMSC: Primary 14; 11
With the recent increase in available computing power, new computations are possible in many areas of arithmetic geometry. To name just a few examples, Cremona's tables of elliptic curves now go up to conductor 120,000 instead of just conductor 1,000, tables of Hilbert class fields are known for discriminant up to at least 5,000, and special values of Hilbert and Siegel modular forms can be calculated to extremely high precision. In many cases, these experimental capabilities have led to new observations and ideas for progress in the field. They have also led to natural algorithmic questions on the feasibility and efficiency of many computations, especially for the purpose of applications in cryptography. The AMS Special Session on Computational Arithmetic Geometry, held on April 29–30, 2006, in San Francisco, CA, gathered together many of the people currently working on the computational and algorithmic aspects of arithmetic geometry. This volume contains research articles related to talks given at the session. The majority of articles are devoted to various aspects of arithmetic geometry, mainly with a computational approach.
ReadershipGraduate students and research mathematicians interested in arithmetic geometry and computational number theory.
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Table of Contents
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Articles
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Jeffrey D. Achter — Results of Cohen-Lenstra type for quadratic function fields [ MR 2459984 ]
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Eric Bach and Denis Charles — The hardness of computing an eigenform [ MR 2459985 ]
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Reinier Bröker and Peter Stevenhagen — Constructing elliptic curves of prime order [ MR 2459986 ]
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Abdulaziz Deajim and David Grant — Space-time codes and non-associative division algebras arising from elliptic curves [ MR 2459987 ]
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Jordan S. Ellenberg — Points of low height on $\Bbb P^1$ over number fields and bounds for torsion in class groups [ MR 2459988 ]
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Everett W. Howe — Supersingular genus-2 curves over fields of characteristic 3 [ MR 2459989 ]
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Kiran S. Kedlaya — Search techniques for root-unitary polynomials [ MR 2459990 ]
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Benjamin Levitt and William McCallum — Yet more elements in the Shafarevich-Tate group of the Jacobian of a Fermat curve [ MR 2459991 ]
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Ken McMurdy — Stable reduction of $X_0(81)$ [ MR 2459992 ]
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Bjorn Poonen — Isomorphism types of commutative algebras of finite rank over an algebraically closed field [ MR 2459993 ]
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Rachel Pries — A short guide to $p$-torsion of abelian varieties in characteristic $p$ [ MR 2459994 ]
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Additional Material
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
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With the recent increase in available computing power, new computations are possible in many areas of arithmetic geometry. To name just a few examples, Cremona's tables of elliptic curves now go up to conductor 120,000 instead of just conductor 1,000, tables of Hilbert class fields are known for discriminant up to at least 5,000, and special values of Hilbert and Siegel modular forms can be calculated to extremely high precision. In many cases, these experimental capabilities have led to new observations and ideas for progress in the field. They have also led to natural algorithmic questions on the feasibility and efficiency of many computations, especially for the purpose of applications in cryptography. The AMS Special Session on Computational Arithmetic Geometry, held on April 29–30, 2006, in San Francisco, CA, gathered together many of the people currently working on the computational and algorithmic aspects of arithmetic geometry. This volume contains research articles related to talks given at the session. The majority of articles are devoted to various aspects of arithmetic geometry, mainly with a computational approach.
Graduate students and research mathematicians interested in arithmetic geometry and computational number theory.
-
Articles
-
Jeffrey D. Achter — Results of Cohen-Lenstra type for quadratic function fields [ MR 2459984 ]
-
Eric Bach and Denis Charles — The hardness of computing an eigenform [ MR 2459985 ]
-
Reinier Bröker and Peter Stevenhagen — Constructing elliptic curves of prime order [ MR 2459986 ]
-
Abdulaziz Deajim and David Grant — Space-time codes and non-associative division algebras arising from elliptic curves [ MR 2459987 ]
-
Jordan S. Ellenberg — Points of low height on $\Bbb P^1$ over number fields and bounds for torsion in class groups [ MR 2459988 ]
-
Everett W. Howe — Supersingular genus-2 curves over fields of characteristic 3 [ MR 2459989 ]
-
Kiran S. Kedlaya — Search techniques for root-unitary polynomials [ MR 2459990 ]
-
Benjamin Levitt and William McCallum — Yet more elements in the Shafarevich-Tate group of the Jacobian of a Fermat curve [ MR 2459991 ]
-
Ken McMurdy — Stable reduction of $X_0(81)$ [ MR 2459992 ]
-
Bjorn Poonen — Isomorphism types of commutative algebras of finite rank over an algebraically closed field [ MR 2459993 ]
-
Rachel Pries — A short guide to $p$-torsion of abelian varieties in characteristic $p$ [ MR 2459994 ]
