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About this book This volume is the first of approximately four volumes devoted to providing statements, proofs, and discussions of all the claims made by Srinivasa Ramanujan in his lost notebook and all his other manuscripts and letters published with the lost notebook. Show all. Table of contents 19 chapters Table of contents 19 chapters Inroduction Pages Other q-continued Fractions Pages Asymptotic Formulas for Continued Fractions Pages The Rogers-Fine Identity Pages Partial Fractions Pages Hadamard Products for Two q-Series Pages Integrals of Theta Functions Pages Incomplete Elliptic Integrals Pages Infinite Integrals of q-Products Pages Fragments on Lambert Series Pages Show next xx.

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Srinivasa Iyengar Ramanujan: A self-taught Mathematician - #knowYourHero - 2

PAGE 1. One distinguishing feature of Kempf's presentation is the systematic use of Mumford's theta group. This allows him to give precise results about the projective ideal of an abelian variety. In its detailed discussion of the cohomology of invertible sheaves, the book incorporates material previously found only in research articles.

Also, several examples where abelian varieties arise in various branches of geometry are given as a conclusion of the book.

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Book It covers a wide range of topics related to hypergeometric functions, thus giving a broad perspective of the state of the art in the field. Enrique Ramirez de Arellano. The Ball and Some Hilbert Problems. Rolf-Peter Holzapfel. As an interesting object of arithmetic, algebraic and analytic geometry the complex ball was born in a paper of the French Mathematician E.

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At first glance the original ideas and the advanced theories seem to be rather disconnected. With these lectures I try to build a bridge from the analytic origins to the actual research on effective problems of arithmetic algebraic geometry. It is dedicated to the construction of number fields by means of special value of transcendental functions of several variables.

The close connection with three other HILBERT problems will be explained together with corresponding advanced theories, which are necessary to find special effective solutions, namely: 7.

Irrationality and Transcendence of Certain Numbers; Generalizations of Thomae's Formula for Zn Curves. Previous publications on the generalization of the Thomae formulae to Zn curves have emphasized the theory's implications in mathematical physics and depended heavily on applied mathematical techniques. This book redevelops these previous results demonstrating how they can be derived directly from the basic properties of theta functions as functions on compact Riemann surfaces.

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In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems. Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity including partition theory and geometric number theory.

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Complex Numbers from A to. Z introduces the reader to this fascinating subject that, from the time of L. Euler, has become one of the most utilized ideas in mathematics. Bruce C. During the years , Ramanujan recorded many of his mathematical discoveries in notebooks without providing proofs.

16 editions of this work

Although many of his results were already in the literature, more were not. Almost a decade after Ramanujan's death in , G. Watson and B.