Computational aspects of modular forms and Galois representations how one can compute in polynomial time the value of Ramanujan's tau at a prime.

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 k...

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Hlavní autoři:	Couveignes, Jean-Marc, Edixhoven, Bas
Médium:	E-kniha Kniha
Jazyk:	angličtina
Vydáno:	Princeton, N.J Princeton University Press 2011
Vydání:	1
Edice:	Annals of Mathematics Studies
Témata:	Absolute value Accuracy and precision Addition Agence nationale de la recherche Algorithm Approximation Arakelov theory Bosman Calculation Characteristic polynomial Class field theory Coefficient Cohomology Combination Complex number Computation Conjugacy class Cusp form Determinant Differential form Discriminant Division by zero Divisor Divisor (algebraic geometry) Eigenform Eigenvalues and eigenvectors Elliptic curve Embedding Equation Exponential function Factorization Finite field Frobenius endomorphism Galois modules (Algebra) GRH Hecke algebra Hecke operator Holomorphic function Integer Irreducible component Jacobian variety Line bundle Linear combination Logarithm MATHEMATICS MATHEMATICS / Geometry / Algebraic MATHEMATICS / Number Theory Maximal ideal Minimal polynomial (field theory) Modular curve Modular form Monic polynomial Morphism Natural number Numerical analysis Polynomial Power series Prime factor Prime number Real number Residue field Riemann surface Ring of integers Schoof's algorithm Scientific notation Series expansion Special case Subgroup Tangent space Theorem Time complexity Turing machine Upper and lower bounds Variable (mathematics) Weil pairing Polynomial Cusp form Differential form Bosman Minimal polynomial (field theory) Turing machine Subgroup Hecke operator Conjugacy class Divisor (algebraic geometry) Combination Eigenvalues and eigenvectors Series expansion Calculation Accuracy and precision Tangent space Discriminant Finite field Addition Approximation Real number Schoof's algorithm Determinant Holomorphic function Cohomology Ring of integers Algorithm Riemann surface Division by zero Numerical analysis Computation Maximal ideal Special case GRH Time complexity Prime number Natural number Weil pairing Characteristic polynomial Residue field Embedding Power series Exponential function Upper and lower bounds Hecke algebra Linear combination Eigenform Logarithm Monic polynomial Theorem Frobenius endomorphism Prime factor Coefficient Irreducible component Line bundle Equation Morphism Modular curve Elliptic curve Factorization Complex number Integer Jacobian variety Variable (mathematics) Arakelov theory Divisor Scientific notation Modular form Agence nationale de la recherche Absolute value
ISBN:	9780691142029, 0691142025, 9780691142012, 0691142017, 9781400839001, 1400839009
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