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Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (Annals of Mathematics Studies)
Published by Princeton University Press, 2011
ISBN 10: 0691142025 ISBN 13: 9780691142029
Language: English
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Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176) (Annals of Mathematics Studies (176))
Published by Princeton University Press, 2011
ISBN 10: 0691142025 ISBN 13: 9780691142029
Language: English
Condition: New.
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Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau At a Prime
Published by Princeton University Press, Princeton, 2011
ISBN 10: 0691142025 ISBN 13: 9780691142029
Language: English
Paperback. Condition: Near Fine. A nice, solid copy. ; Annals Of Mathematics Studies; Vol. 176; 6.5 X 1 X 9.5 inches; 425 pages.
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Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau At a Prime
Published by Princeton University Press, Princeton, 2011
ISBN 10: 0691142025 ISBN 13: 9780691142029
Language: English
Paperback. Condition: Near Fine. A nice, solid copy. ; Annals of Mathematics Studies; Vol. 176; 6.5 X 1 X 9.5 inches; 425 pages.
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Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176) (Annals of Mathematics Studies (176))
Published by Oxford University Press, 2011
ISBN 10: 0691142017 ISBN 13: 9780691142012
Language: English
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Introduction to Applications of Modular Forms: Computational Aspects
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Condition: New. 1st ed. 2023 edition NO-PA16APR2015-KAP.
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Introduction to Applications of Modular Forms Computational Aspects
Published by Springer International Publishing AG, 2023
ISBN 10: 3031326288 ISBN 13: 9783031326288
Language: English
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Computational Aspects of Modular Forms and Galois Representations : How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime
Published by Princeton University Press, 2011
ISBN 10: 0691142025 ISBN 13: 9780691142029
Language: English
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Computational Aspects of Modular Forms and Galois Representations
Published by Princeton University Press, 2011
ISBN 10: 0691142025 ISBN 13: 9780691142029
Language: English
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Computational Aspects of Modular Forms and Galois Representations : How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime
Published by Princeton University Press, 2011
ISBN 10: 0691142025 ISBN 13: 9780691142029
Language: English
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Introduction to Applications of Modular Forms : Computational Aspects
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Computational Aspects of Modular Forms and Galois Representations- How One can Compute in Polynomial of Ramanujan`s Tau at a Prime
Published by Princeton University Press, 2011
ISBN 10: 0691142025 ISBN 13: 9780691142029
Language: English
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Introduction to Applications of Modular Forms: Computational Aspects (Synthesis Lectures on Mathematics & Statistics)
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Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan?s Tau at a Prime (AM-176)
Published by Princeton University Press, 2011
ISBN 10: 0691142025 ISBN 13: 9780691142029
Language: English
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Add to basketCondition: New. Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. This title gives an algorithm for computing coefficients of modular forms of level one in polynomial time. Editor(s): Edixhoven, Bas; Couveignes, Jean-Marc. Series: Annals of Mathematics Studies. Num Pages: 440 pages, 6 line illus. BIC Classification: PBH; PBMW. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 234 x 157 x 22. Weight in Grams: 622. . 2011. Paperback. . . . .
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Computational Aspects of Modular Forms and Galois Representations : How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime
Published by Princeton University Press, 2011
ISBN 10: 0691142025 ISBN 13: 9780691142029
Language: English
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Introduction to Applications of Modular Forms : Computational Aspects
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Computational Aspects of Modular Forms and Galois Representations : How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime
Published by Princeton University Press, 2011
ISBN 10: 0691142025 ISBN 13: 9780691142029
Language: English
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Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (Annals of Mathematics Studies, 176)
Published by Princeton University Press, 2011
ISBN 10: 0691142025 ISBN 13: 9780691142029
Language: English
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Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)
Published by Princeton University Press, 2011
ISBN 10: 0691142025 ISBN 13: 9780691142029
Language: English
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Computational Aspects of Modular Forms and Galois Representations
Published by Princeton University Press, US, 2011
ISBN 10: 0691142025 ISBN 13: 9780691142029
Language: English
Paperback. Condition: New. Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number p can be computed in time bounded by a fixed power of the logarithm of p. Such fast computation of Fourier coefficients is itself based on the main result of the book: the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program.The computation of the Galois representations uses their realization, following Shimura and Deligne, in the torsion subgroup of Jacobian varieties of modular curves. The main challenge is then to perform the necessary computations in time polynomial in the dimension of these highly nonlinear algebraic varieties. Exact computations involving systems of polynomial equations in many variables take exponential time. This is avoided by numerical approximations with a precision that suffices to derive exact results from them. Bounds for the required precision--in other words, bounds for the height of the rational numbers that describe the Galois representation to be computed--are obtained from Arakelov theory. Two types of approximations are treated: one using complex uniformization and another one using geometry over finite fields. The book begins with a concise and concrete introduction that makes its accessible to readers without an extensive background in arithmetic geometry. And the book includes a chapter that describes actual computations.
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Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan s Tau at a Prime (AM-176)
Published by Princeton University Press, 2011
ISBN 10: 0691142025 ISBN 13: 9780691142029
Language: English
Condition: New. Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. This title gives an algorithm for computing coefficients of modular forms of level one in polynomial time. Editor(s): Edixhoven, Bas; Couveignes, Jean-Marc. Series: Annals of Mathematics Studies. Num Pages: 440 pages, 6 line illus. BIC Classification: PBH; PBMW. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 234 x 157 x 22. Weight in Grams: 622. . 2011. Paperback. . . . . Books ship from the US and Ireland.
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Add to basketHardcover. Condition: Brand New. 179 pages. 9.45x6.61x0.63 inches. In Stock.
