FUNCTION FIELD ARITHMETIC
by Dinesh S Thakur (University of Arizona, USA)
About the Author Dinesh S Thakur got his doctorate from Harvard University in 1987. He has spent 3 years each in research at the Institute for Advanced Study, Princeton and at the Tata Institute of Fundamental Research, Bombay. Currently, he is a Professor of Mathematics at University of Arizona.
This book provides an exposition of function field arithmetic with emphasis on recent developments concerning Drinfeld modules, the arithmetic of special values of transcendental functions (such as zeta and gamma functions and their interpolations), diophantine approximation and related interesting open problems. While it covers many topics treated in 'Basic Structures of Function Field Arithmetic' by David Goss, it complements that book with the inclusion of recent developments as well as the treatment of new topics such as diophantine approximation, hypergeometric functions, modular forms, transcendence, automata and solitons. There is also new work on multizeta values and log-algebraicity. The author has included numerous worked-out examples. Many open problems, which can serve as good thesis problems, are discussed.
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