By Shigeru Kanemitsu,Chaohua Jia
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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 less than the help of the Japan Society for the merchandising of technology (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 celebration of the convention on the learn Institute of Mathematical Sciences (RIMS), Kyoto collage.
Modular types are vastly very important in a number of parts of arithmetic, from quantity thought and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a customary instance, have deep mathematics importance. sooner than this ebook, the quickest identified algorithms for computing those Fourier coefficients took exponential time, other than in a few distinctive instances.
The invited papers gathered during this quantity tackle subject matters on the topic of the examine of Raman Parimala (plenary speaker on the upcoming ICM 2010). those issues concentration totally on the interaction among algebra, quantity idea, and algebraic geometry. The integrated contributions conceal fascinating study in components corresponding to 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 proper paintings embraces vital issues in research and algebra from a problem-solving point of view. The publication is based to aid the reader in formulating and proving conjectures, in addition to devising ideas to special mathematical difficulties by way of making connections among a number of techniques and ideas from various components of arithmetic.
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