By Antoine Chambert-Loir
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This quantity includes the lawsuits of the very profitable moment China-Japan Seminar held in lizuka, Fukuoka, Japan, in the course of March 12-16, 2001 below the aid of the Japan Society for the merchandising of technology (JSPS) and the nationwide technological know-how starting place of China (NSFC), and a few invited papers of eminent number-theorists who visited Japan in the course of 1999-2001 on the get together of the convention on the learn Institute of Mathematical Sciences (RIMS), Kyoto collage.
Modular types are greatly very important in a number of components of arithmetic, from quantity conception and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a standard instance, have deep mathematics importance. sooner than this e-book, the quickest identified algorithms for computing those Fourier coefficients took exponential time, other than in a few exact circumstances.
The invited papers amassed during this quantity deal with themes concerning the learn of Raman Parimala (plenary speaker on the upcoming ICM 2010). those subject matters concentration totally on the interaction among algebra, quantity thought, and algebraic geometry. The integrated contributions disguise intriguing study in parts similar to box patching and an explanation of the Serre's Conjecture II for functionality fields of advanced surfaces.
Construction bridges among classical effects and modern nonstandard difficulties, this hugely proper paintings embraces very important issues in research and algebra from a problem-solving point of view. The publication is established to aid the reader in formulating and proving conjectures, in addition to devising ideas to special mathematical difficulties via making connections among a number of thoughts and concepts from diversified components of arithmetic.
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