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| Author | : Jeffrey Stopple |
| Publisher | : Cambridge University Press |
| Total Pages | : 404 |
| Release | : 2003-06-23 |
| Genre | : Mathematics |
| ISBN | : 9780521012539 |
An undergraduate-level 2003 introduction whose only prerequisite is a standard calculus course.
| Author | : Jeffrey Stopple |
| Publisher | : Cambridge University Press |
| Total Pages | : 398 |
| Release | : 2003-06-23 |
| Genre | : Mathematics |
| ISBN | : 9780521813099 |
This undergraduate-level introduction describes those mathematical properties of prime numbers that can be deduced with the tools of calculus. Jeffrey Stopple pays special attention to the rich history of the subject and ancient questions on polygonal numbers, perfect numbers and amicable pairs, as well as to the important open problems. The culmination of the book is a brief presentation of the Riemann zeta function, which determines the distribution of prime numbers, and of the significance of the Riemann Hypothesis.
| Author | : John Knopfmacher |
| Publisher | : Courier Dover Publications |
| Total Pages | : 356 |
| Release | : 2015-03-17 |
| Genre | : Mathematics |
| ISBN | : 0486169340 |
Innovative study applies classical analytic number theory to nontraditional subjects. Covers arithmetical semigroups and algebraic enumeration problems, arithmetical semigroups with analytical properties of classical type, and analytical properties of other arithmetical systems. 1975 edition.
| Author | : Bateman Paul Trevier |
| Publisher | : World Scientific |
| Total Pages | : 376 |
| Release | : 2004-09-07 |
| Genre | : Mathematics |
| ISBN | : 9814365564 |
This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable (”elementary”) and complex variable (”analytic”) methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.Comments and corrigenda for the book are found at www.math.uiuc.edu/~diamond/.
| Author | : M. Ram Murty |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 162 |
| Release | : 2009-02-09 |
| Genre | : Mathematics |
| ISBN | : 0821847740 |
This book is an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises included, it will acquaint the non-expert to the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of $p$-adic $L$-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences. These congruences are then used to construct the $p$-adic analog of the Riemann zeta function and $p$-adic analogs of Dirichlet's $L$-functions. Featured is a chapter on how to apply the theory of Newton polygons to determine Galois groups of polynomials over the rational number field. As motivation for further study, the final chapter introduces Iwasawa theory.
| Author | : A. G. Postnikov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 332 |
| Release | : 1988-12-31 |
| Genre | : Mathematics |
| ISBN | : 0821813498 |
Aimed at a level between textbooks and the latest research monographs, this book is directed at researchers, teachers, and graduate students interested in number theory and its connections with other branches of science. Choosing to emphasize topics not sufficiently covered in the literature, the author has attempted to give as broad a picture as possible of the problems of analytic number theory.
| Author | : Donald J. Newman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 80 |
| Release | : 2006-04-18 |
| Genre | : Mathematics |
| ISBN | : 0387227407 |
Some of the central topics in number theory, presnted in a simple and concise fashion. The author covers an amazing amount of material, despite a leisurely pace and emphasis on readability. His heartfelt enthusiasm enables readers to see what is magical about the subject. All the topics are presented in a refreshingly elegant and efficient manner with clever examples and interesting problems throughout. The text is suitable for a graduate course in analytic number theory.
| Author | : Heng Huat Chan |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 128 |
| Release | : 2009-04-21 |
| Genre | : Mathematics |
| ISBN | : 9814365270 |
This book is written for undergraduates who wish to learn some basic results in analytic number theory. It covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression. The materials in this book are based on A Hildebrand's 1991 lectures delivered at the University of Illinois at Urbana-Champaign and the author's course conducted at the National University of Singapore from 2001 to 2008.
| Author | : Anatolij A. Karatsuba |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 234 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642580181 |
This English translation of Karatsuba's Basic Analytic Number Theory follows closely the second Russian edition, published in Moscow in 1983. For the English edition, the author has considerably rewritten Chapter I, and has corrected various typographical and other minor errors throughout the the text. August, 1991 Melvyn B. Nathanson Introduction to the English Edition It gives me great pleasure that Springer-Verlag is publishing an English trans lation of my book. In the Soviet Union, the primary purpose of this monograph was to introduce mathematicians to the basic results and methods of analytic number theory, but the book has also been increasingly used as a textbook by graduate students in many different fields of mathematics. I hope that the English edition will be used in the same ways. I express my deep gratitude to Professor Melvyn B. Nathanson for his excellent translation and for much assistance in correcting errors in the original text. A.A. Karatsuba Introduction to the Second Russian Edition Number theory is the study of the properties of the integers. Analytic number theory is that part of number theory in which, besides purely number theoretic arguments, the methods of mathematical analysis play an essential role.
| Author | : KRANTZ |
| Publisher | : Birkhäuser |
| Total Pages | : 190 |
| Release | : 2013-03-09 |
| Genre | : Science |
| ISBN | : 3034876440 |
The subject of real analytic functions is one of the oldest in mathe matical analysis. Today it is encountered early in ones mathematical training: the first taste usually comes in calculus. While most work ing mathematicians use real analytic functions from time to time in their work, the vast lore of real analytic functions remains obscure and buried in the literature. It is remarkable that the most accessible treatment of Puiseux's theorem is in Lefschetz's quite old Algebraic Geometry, that the clearest discussion of resolution of singularities for real analytic manifolds is in a book review by Michael Atiyah, that there is no comprehensive discussion in print of the embedding prob lem for real analytic manifolds. We have had occasion in our collaborative research to become ac quainted with both the history and the scope of the theory of real analytic functions. It seems both appropriate and timely for us to gather together this information in a single volume. The material presented here is of three kinds. The elementary topics, covered in Chapter 1, are presented in great detail. Even results like a real ana lytic inverse function theorem are difficult to find in the literature, and we take pains here to present such topics carefully. Topics of middling difficulty, such as separate real analyticity, Puiseux series, the FBI transform, and related ideas (Chapters 2-4), are covered thoroughly but rather more briskly.
