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0 (hodnocen0 x )

EB

ONLINE

Princeton, N.J. : Princeton University Press, c2011

1 online resource (xi, 425 p.) : ill

ISBN 9781400839001 (electronic bk.)

ISBN 9780691142012 (hardback)

ISBN 9780691142029 (pbk.)

Annals of mathematics studies ; 176

"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.-.

"This book represents a major step forward from explicit class field theory, and it could be described as the start of the ’explicit Langlands program’"-- Provided by publisher..

Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries

001725641

full

(Au-PeEL)EBL670341

(CaONFJC)MIL305180

(CaPaEBR)ebr10456327

(MiAaPQ)EBC670341

(OCoLC)729386470