Overview

The book discusses major topics in complex analysis with applications to number theory. This book is intended as a text for graduate students of mathematics and undergraduate students of engineering, as well as to researchers in complex analysis and number theory. This theory is a prerequisite for the study of many areas of mathematics, including the theory of several finitely and infinitely many complex variables, hyperbolic geometry, two and three manifolds and number theory. In additional to solved examples and problems, the book covers most of the topics of current interest, such as Cauchy theorems, Picard’s theorems, Riemann–Zeta function, Dirichlet theorem, gamma function and harmonic functions. 

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9789811590962

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Reviews

The book can serve as a reference source for readers interested in mathematical relations between complex analysis and number theory. Also, it can attract amateurs of classical conjectures for the Riemann zeta function. (Dmitri V. Prokhorov, zbMATH 1467.30001, 2021)

The strength of this text is in its concise but complete development of each topic. ... Shorey's text is best used for a second complex analysis course covering a range of advanced topics ... . (Ian Whitehead, MAA Reviews, January 10, 2022) The book can serve as a reference source for readers interested in mathematical relations between complex analysis and number theory. Also, it can attract amateurs of classical conjectures for the Riemann zeta function. (Dmitri V. Prokhorov, zbMATH 1467.30001, 2021)

Author Information

TARLOK NATH SHOREY is a distinguished professor at the National Institute of Advanced Studies (situated in the campus of the Indian Institute of Science), Bengaluru, India. Earlier, he taught at the Department of Mathematics, Indian Institute of Technology Bombay, India. He also had been associated with the Tata Institute of Fundamental Research (TIFR), Mumbai, India, for a period of 42 years. Professor Shorey has done numerous momentous works on transcendental number theory and Diophantine equation. In 1987, he was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology—the highest science award in India—in the Mathematical Sciences category. He has coauthored a book, Exponential Diophantine Equations, and has more than 142 research publications to his credit. He is fellow of the Indian National Science Academy (INSA), Indian Academy of Sciences (IASc) and The National Academy of Sciences (NASI).

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