By H. P. F. Swinnerton-Dyer
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This quantity includes the complaints of the very winning moment China-Japan Seminar held in lizuka, Fukuoka, Japan, in the course of March 12-16, 2001 below the help of the Japan Society for the advertising of technological know-how (JSPS) and the nationwide technological know-how beginning 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 study Institute of Mathematical Sciences (RIMS), Kyoto collage.
Modular varieties are drastically vital in a variety of parts of arithmetic, from quantity idea and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a regular instance, have deep mathematics value. sooner than this e-book, the quickest identified algorithms for computing those Fourier coefficients took exponential time, other than in a few detailed instances.
The invited papers accumulated during this quantity deal with themes concerning the examine of Raman Parimala (plenary speaker on the upcoming ICM 2010). those topics concentration totally on the interaction among algebra, quantity thought, and algebraic geometry. The integrated contributions conceal fascinating examine in parts resembling box patching and an explanation of the Serre's Conjecture II for functionality fields of complicated surfaces.
Development bridges among classical effects and modern nonstandard difficulties, this hugely correct paintings embraces vital subject matters in research and algebra from a problem-solving standpoint. The publication is established to aid the reader in formulating and proving conjectures, in addition to devising options to big mathematical difficulties by way of making connections among numerous techniques and ideas from diversified components of arithmetic.
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