Computational aspects modular forms galois (28 risultati)
Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau At a Prime
De Jong, Robin & Franz Merkl & Johan Bosman & Jean-Marc Couveignes & Bas Edixhoven
Lingua: Inglese
Editore: Princeton University Press, Princeton, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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Paperback. Condizione: Near Fine. A nice, solid copy. ; Annals Of Mathematics Studies; Vol. 176; 6.5 X 1 X 9.5 inches; 425 pages.
Lingua: Inglese
Editore: Princeton University Press, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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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
Edixhoven, Bas & Jean-Marc Couveignes & Robin De Jong & Franz Merkl & Johan Bosman
Lingua: Inglese
Editore: Princeton University Press, Princeton, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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Paperback. Condizione: Near Fine. A nice, solid copy. ; Annals of Mathematics Studies; Vol. 176; 6.5 X 1 X 9.5 inches; 425 pages.
Lingua: Inglese
Editore: Oxford University Press, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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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
Edixhoven, Bas (EDT); Couveignes, Jean-marc (EDT); Bosman, Johan (CON); De Jong, Robin (CON); Merkl, Franz (CON)
Lingua: Inglese
Editore: Princeton University Press, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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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
Edixhoven, Bas (EDT); Couveignes, Jean-marc (EDT); Bosman, Johan (CON); De Jong, Robin (CON); Merkl, Franz (CON)
Lingua: Inglese
Editore: Princeton University Press, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
- Brossura
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Editore: Princeton University Press, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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Condizione: 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: A…nnals 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. . . . .
Computational Aspects of Modular Forms and Galois Representations : How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime
Edixhoven, Bas (EDT); Couveignes, Jean-marc (EDT); Bosman, Johan (CON); De Jong, Robin (CON); Merkl, Franz (CON)
Lingua: Inglese
Editore: Princeton University Press, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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Paperback. Condizione: 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 al…gorithms 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.
Computational Aspects of Modular Forms and Galois Representations : How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime
Edixhoven, Bas (EDT); Couveignes, Jean-marc (EDT); Bosman, Johan (CON); De Jong, Robin (CON); Merkl, Franz (CON)
Lingua: Inglese
Editore: Princeton University Press, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
- Brossura
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Lingua: Inglese
Editore: Princeton University Press, US, 2011
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Paperback. Condizione: 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 al…gorithms 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.
Computational Aspects of Modular forms and Galois Representations
Merkl Franz Couveignes Jean?marc Couveignes Jean-marc Bosman Johan De Jong Robin Edixhoven Bas
Lingua: Inglese
Editore: Princeton University Press, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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Condizione: New. pp. 440.
Lingua: Inglese
Editore: Princeton University Press, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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Condizione: 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: A…nnals 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.
Lingua: Inglese
Editore: Princeton University Press, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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Computational Aspects of Modular forms and Galois Representations
Franz Merkl Jean?marc Couveignes Jean-marc Couveignes Johan Bosman Robin De Jong Bas Edixhoven
Lingua: Inglese
Editore: Princeton University Press, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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Condizione: New. pp. 440.
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Editore: Princeton University Press, US, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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Paperback. Condizione: 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 al…gorithms 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.
Lingua: Inglese
Editore: Princeton Univ Pr, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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Paperback. Condizione: 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 al…gorithms 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.
Lingua: Inglese
Editore: Oxford University Press, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 f…orms of level one in polynomial time.
Lingua: Inglese
Editore: Princeton University Press, 2011
Serie: Annals of Mathematics Studies, Libro 28 di 202. Libro 28 di 202 - Annals of Mathematics Studies
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Taschenbuch. Condizione: Neu. Computational Aspects of Modular Forms and Galois Representations | How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime | Bas Edixhoven (u. a.) | Taschenbuch | Einband - flex.(Paperback) | Englisch | 2011 | Princeton University Press | EAN 9780691142029 | Verantwortliche P…erson für die EU: Libri GmbH, Europaallee 1, 36244 Bad Hersfeld, gpsr[at]libri[dot]de | Anbieter: preigu Print on Demand.
Lingua: Inglese
Editore: Princeton University Press, 2011
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Taschenbuch. Condizione: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - 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.
