Harmonic Analysis, the Trace Formula, and Shimura Varieties
by J. Arthur, D. Ellwood, R. Kottwitz
Publisher: American Mathematical Society 2005
Number of pages: 706
The goal of this volume is to provide an entry point into the exciting and challenging field of the modern theory of automorphic forms. It is directed on the one hand at graduate students and professional mathematicians who would like to work in the area.
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by J. E. Cremona - Cambridge University Press
The author describes the construction of modular elliptic curves giving an algorithm for their computation. Then algorithms for the arithmetic of elliptic curves are presented. Finally, the results of the implementations of the algorithms are given.
by A. Genestier, B.C. Ngo
The goal of these lectures is to explain the representability of moduli space abelian varieties with polarization, endomorphism and level structure, due to Mumford and the description of the set of its points over a finite field, due to Kottwitz.
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An examination of some of the problems posed by Florentin Smarandache. The problems are from different areas, such as sequences, primes and other aspects of number theory. The problems are solved in the book, or the author raises new questions.
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The book based on lecture notes of a course given at Princeton University in 1980. From the contents: the impredicativity of induction, the axioms of arithmetic, order, induction by relativization, the bounded least number principle, and more.