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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)
Bas Edixhoven
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€ 69.64
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Description for 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)
Paperback. 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.
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 ... Read more
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 ... Read more
Product Details
Format
Paperback
Publication date
2011
Publisher
Princeton University Press United States
Number of pages
440
Condition
New
Series
Annals of Mathematics Studies
Number of Pages
440
Place of Publication
New Jersey, United States
ISBN
9780691142029
SKU
V9780691142029
Shipping Time
Usually ships in 7 to 11 working days
Ref
99-1
About Bas Edixhoven
Bas Edixhoven is professor of mathematics at the University of Leiden. Jean-Marc Couveignes is professor of mathematics at the University of Toulouse le Mirail. Robin de Jong is assistant professor at the University of Leiden. Franz Merkl is professor of applied mathematics at the University of Munich. Johan Bosman is a postdoctoral researcher at the Institut fur Experimentelle Mathematik in ... Read more
Reviews for 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)
"The book is well written and provides sufficient detail and reminders about the big picture. It gives a nice exposition of the material involved and should be accessible to graduate students or researchers with a sufficient background in number theory and algebraic geometry."
Jeremy A. Rouse, Mathematical Reviews Clippings
Jeremy A. Rouse, Mathematical Reviews Clippings