Jianya Liu's Books

Number Theory

Dreaming in Dreams : Proceedings of the 5th China-Japan Seminar : Higashi-Osaka, Japan 27-31 August 2008

By: Takashi Aoki,Shigeru Kanemitsu,Jianya Liu

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Number Theory

Dreaming in Dreams : Proceedings of the 5th China-Japan Seminar : Higashi-Osaka, Japan 27-31 August 2008

By: Takashi Aoki,Shigeru Kanemitsu,Jianya Liu

This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory. Kitaoka's paper is a continuation of his earlier paper published in the last proceedings and pushes the research forward. Browning's paper introduces a new direction of research on analytic number theory ? quantitative theory of some surfaces and Bruedern et al's paper details state-of-the-art affairs of additive number theory. There are two papers on modular forms ? Kohnen's paper describes generalized modular forms (GMF) which has some applications in conformal field theory, while Liu's paper is very useful for readers who want to have a quick introduction to Maass forms and some analytic-number-theoretic problems related to them. Matsumoto et al's paper gives a very thorough survey on functional relations of root system zeta-functions, Hoshi?Miyake's paper is a continuation of Miyake's long and fruitful research on generic polynomials and gives rise to related Diophantine problems, and Jia's paper surveys some dynamical aspects of a special arithmetic function connected with the distribution of prime numbers. There are two papers of collections of problems by Shparlinski on exponential and character sums and Schinzel on polynomials which will serve as an aid for finding suitable research problems. Yamamura's paper is a complete bibliography on determinant expressions for a certain class number and will be useful to researchers.Thus the book gives a good-balance of classical and modern aspects in number theory and will be useful to researchers including enthusiastic graduate students.

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Page Count

267

Publisher

World Scientific

Published Date

ISBN 10

9814289841

ISBN 13

9789814289849

Analysis And Beyond: An Introduction With Examples And Exercises

By: Shigeru Kanemitsu,Takako Kuzumaki,Jianya Liu

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Analysis And Beyond: An Introduction With Examples And Exercises

By: Shigeru Kanemitsu,Takako Kuzumaki,Jianya Liu

This volume aims to bridge between elementary textbooks on calculus and established books on advanced analysis. It provides elucidation of the reversible process of differentiation and integration through two featured principles: the chain rule and its inverse — the change of variable — as well as the Leibniz rule and its inverse — the integration by parts. The chain rule or differentiation of composite functions is ubiquitous since almost all (a.a.) functions are composite functions of (elementary) functions and with the change of variable method as its reverse process. The Leibniz rule or differentiation of the product of two functions is essential since it makes differentiation nonlinear and with the method of integration by parts as its reverse process.Readers will find numerous worked-out examples and exercises in this volume. Detailed solutions are provided for most of the common exercises so that readers remain enthusiastically motivated in solving and understanding the concepts better.The intention of this volume is to lead the reader into the rich fields of advanced analysis and to obtain a much better view of useful mathematics.

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Page Count

328

Publisher

World Scientific

Published Date

ISBN 10

9811224501

ISBN 13

9789811224508

Number Theory

Arithmetic in Shangri-La : Proceedings of the 6th China-Japan Seminar, Shanghai, China, 15-17 August 2011

By: Shigeru Kanemitsu,Hongze Li,Jianya Liu

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Number Theory

Arithmetic in Shangri-La : Proceedings of the 6th China-Japan Seminar, Shanghai, China, 15-17 August 2011

By: Shigeru Kanemitsu,Hongze Li,Jianya Liu

This volume is based on the successful 6th ChinaOCoJapan Seminar on number theory that was held in Shanghai Jiao Tong University in August 2011. It is a compilation of survey papers as well as original works by distinguished researchers in their respective fields. The topics range from traditional analytic number theory OCo additive problems, divisor problems, Diophantine equations OCo to elliptic curves and automorphic L-functions. It contains new developments in number theory and the topics complement the existing two volumes from the previous seminars which can be found in the same book series.

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Page Count

273

Publisher

World Scientific

Published Date

ISBN 10

9814452459

ISBN 13

9789814452458

Analysis And Beyond: An Introduction With Examples And Exercises

By: Shigeru Kanemitsu,Takako Kuzumaki,Jianya Liu

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Analysis And Beyond: An Introduction With Examples And Exercises

By: Shigeru Kanemitsu,Takako Kuzumaki,Jianya Liu

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

328

Publisher

World Scientific

Published Date

ISBN 10

9811224501

ISBN 13

9789811224508

Number Theory

Dreaming in Dreams : Proceedings of the 5th China-Japan Seminar : Higashi-Osaka, Japan 27-31 August 2008

By: Takashi Aoki,Shigeru Kanemitsu,Jianya Liu

Write a review Read reviews Take a Quiz Solve Book Puzzle

Number Theory

Dreaming in Dreams : Proceedings of the 5th China-Japan Seminar : Higashi-Osaka, Japan 27-31 August 2008

By: Takashi Aoki,Shigeru Kanemitsu,Jianya Liu

This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory. Kitaoka''s paper is a continuation of his earlier paper published in the last proceedings and pushes the research forward. Browning''s paper introduces a new direction of research on analytic number theory OCo quantitative theory of some surfaces and Bruedern et al ''s paper details state-of-the-art affairs of additive number theory. There are two papers on modular forms OCo Kohnen''s paper describes generalized modular forms (GMF) which has some applications in conformal field theory, while Liu''s paper is very useful for readers who want to have a quick introduction to Maass forms and some analytic-number-theoretic problems related to them. Matsumoto et al ''s paper gives a very thorough survey on functional relations of root system zeta-functions, HoshiOCoMiyake''s paper is a continuation of Miyake''s long and fruitful research on generic polynomials and gives rise to related Diophantine problems, and Jia''s paper surveys some dynamical aspects of a special arithmetic function connected with the distribution of prime numbers. There are two papers of collections of problems by Shparlinski on exponential and character sums and Schinzel on polynomials which will serve as an aid for finding suitable research problems. Yamamura''s paper is a complete bibliography on determinant expressions for a certain class number and will be useful to researchers. Thus the book gives a good-balance of classical and modern aspects in number theory and will be useful to researchers including enthusiastic graduate students. Sample Chapter(s). Chapter 1: Resent Progress on the Quantitative Arithmetic of Del Pezzo Surfaces (329 KB). Contents: Recent Progress on the Quantitative Arithmetic of Del Pezzo Surfaces (T D Browning); Additive Representation in Thin Sequences, VIII: Diophantine Inequalities in Review (J Brdern et al.); Recent Progress on Dynamics of a Special Arithmetic Function (C-H Jia); Some Diophantine Problems Arising from the Isomorphism Problem of Generic Polynomials (A Hoshi & K Miyake); A Statistical Relation of Roots of a Polynomial in Different Local Fields II (Y Kitaoka); Generalized Modular Functions and Their Fourier Coefficients (W Kohnen); Functional Relations for Zeta-Functions of Root Systems (Y Komori et al.); A Quick Introduction to Maass Forms (J-Y Liu); The Number of Non-Zero Coefficients of a Polynomial-Solved and Unsolved Problems (A Schinzel); Open Problems on Exponential and Character Sums (I E Shparlinski); Errata to OC A General Modular Relation in Analytic Number TheoryOCO (H Tsukada); Bibliography on Determinantal Expressions of Relative Class Numbers of Imaginary Abelian Number Fields (K Yamamura). Readership: Graduate students and researchers in mathematics.

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Solve jigsaw puzzle

Age

Page Count

267

Publisher

World Scientific

Published Date

ISBN 10

9814289922

ISBN 13

9789814289924

Book's by Jianya Liu

Number Theory

Number Theory

Analysis And Beyond: An Introduction With Examples And Exercises

Analysis And Beyond: An Introduction With Examples And Exercises

Number Theory

Number Theory

Analysis And Beyond: An Introduction With Examples And Exercises

Analysis And Beyond: An Introduction With Examples And Exercises

Number Theory

Number Theory

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