{"title":"Komaravolu Chandrasekharan","description":null,"products":[{"product_id":"introduction-to-analytic-number-theory-book-komaravolu-chandrasekharan-9783642461262","title":"Introduction to Analytic Number Theory","description":"This book has grown out of a course of lectures I have given at the Eidgenossische Technische Hochschule, Zurich. Notes of those lectures, prepared for the most part by assistants, have appeared in German. This book follows the same general plan as those notes, though in style, and in text (for instance, Chapters III, V, VIII), and in attention to detail, it is rather different. Its purpose is to introduce the non-specialist to some of the fundamental results in the theory of numbers, to show how analytical methods of proof fit into the theory, and to prepare the ground for a subsequent inquiry into deeper questions. It is pub­ lished in this series because of the interest evinced by Professor Beno Eckmann. I have to acknowledge my indebtedness to Professor Carl Ludwig Siegel, who has read the book, both in manuscript and in print, and made a number of valuable criticisms and suggestions. Professor Raghavan Narasimhan has helped me, time and again, with illuminating comments. Dr. Harold Diamond has read the proofs, and helped me to remove obscurities. I have to thank them all. K.C.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49739240931601,"sku":"NGR9783642461262","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52633998819601,"sku":"NLS9783642461262","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642461263.jpg?v=1751253678"},{"product_id":"hermann-weyl-1885-1985-book-komaravolu-chandrasekharan-9783540168430","title":"Hermann Weyl: 1885-1985","description":"Published for the Eidgenossische Technische Hochschule Zurich","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52148697694481,"sku":"NLS9783540168430","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52761582403857,"sku":"NIN9783540168430","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540168430.jpg?v=1757604367"},{"product_id":"elliptic-functions-book-komaravolu-chandrasekharan-9783540152958","title":"Elliptic Functions","description":"This book has grown out of a course of lectures on elliptic functions, given in German, at the Swiss Federal Institute of Technology, Zurich, during the summer semester of 1982. Its aim is to give some idea of the theory of elliptic functions, and of its close connexion with theta-functions and modular functions, and to show how it provides an analytic approach to the solution of some classical problems in the theory of numbers. It comprises eleven chapters. The first seven are function-theoretic, and the next four concern arithmetical applications. There are Notes at the end of every chapter, which contain references to the literature, comments on the text, and on the ramifications, old and new, of the problems dealt with, some of them extending into cognate fields. The treatment is self-contained, and makes no special demand on the reader's knowledge beyond the elements of complex analysis in one variable, and of group theory.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52331826872593,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52331827560721,"sku":"NLS9783540152958","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540152958.jpg?v=1758149589"},{"product_id":"elliptic-functions-book-komaravolu-chandrasekharan-9783642522468","title":"Elliptic Functions","description":"This book has grown out of a course of lectures on elliptic functions, given in German, at the Swiss Federal Institute of Technology, Zurich, during the summer semester of 1982. Its aim is to give some idea of the theory of elliptic functions, and of its close connexion with theta-functions and modular functions, and to show how it provides an analytic approach to the solution of some classical problems in the theory of numbers. It comprises eleven chapters. The first seven are function-theoretic, and the next four concern arithmetical applications. There are Notes at the end of every chapter, which contain references to the literature, comments on the text, and on the ramifications, old and new, of the problems dealt with, some of them extending into cognate fields. The treatment is self-contained, and makes no special demand on the reader's knowledge beyond the elements of complex analysis in one variable, and of group theory.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52429092946193,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52429093667089,"sku":"NLS9783642522468","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642522468.jpg?v=1759166015"},{"product_id":"classical-fourier-transforms-book-komaravolu-chandrasekharan-9783540502487","title":"Classical Fourier Transforms","description":"In gratefuZ remerribrance of Marston Morse and John von Neumann This text formed the basis of an optional course of lectures I gave in German at the Swiss Federal Institute of Technology (ETH), Zlirich, during the Wintersemester of 1986-87, to undergraduates whose interests were rather mixed, and who were supposed, in general, to be acquainted with only the rudiments of real and complex analysis. The choice of material and the treatment were linked to that supposition. The idea of publishing this originated with Dr. Joachim Heinze of Springer- Verlag. I have, in response, checked the text once more, and added some notes and references. My warm thanks go to Professor Raghavan Narasimhan and to Dr. Albert Stadler, for their helpful and careful scrutiny of the manuscript, which resulted in the removal of some obscurities, and to Springer-Verlag for their courtesy and cooperation. I have to thank Dr. Stadler also for his assistance with the diagrams and with the proof-reading. Zlirich, September, 1987 K. C. Contents Chapter I. Fourier transforms on L (-oo, oo) 1 1. Basic properties and examples -. -----. . --. . -. -. . . -. -. . -. . . . - 1 2. The L 1-algebra --. . . . . . . ----. . --. -. . --. . --. . -. . . --. . . . --. -. . 16 3. Differentiabili ty properties . . . ---. -. -------. . . . ----. -. . . -. 18 4. Localization, Mellin transforms . . . . . . -. -. . . . . . -. . . . . . -. . -. . 25 5. Fourier series and Poisson's summation formula . . . . . . . --. --. . 32 6. The uniqueness theorem . . . . . . . -. . . . . . . . . . . -. . . . -. . . . . . . . . . . .","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52660001997073,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52660003176721,"sku":"NLS9783540502487","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540502487.jpg?v=1762264285"},{"product_id":"einfuhrung-in-die-analytische-zahlentheorie-book-komaravolu-chandrasekharan-9783540036111","title":"Einführung in die Analytische Zahlentheorie","description":"Diese Arbeit ist eine Zusammenfassung der Vorlesung, die ich im Wintersemester 1965\/66 in englischer Sprache an der E.T.H. gehalten habe. Herr J. Steinig hat sie sorgf~itigst in der Vortragssprache abgefasst und ins Deutsche Gbertragen. Die Herren M. BrGhlmann, H. Leutwiler und U. Suter haben den deutschen Text freundlichst dur- gelesen und an seiner endgGltigen, stilgerechten Fassung mitgearbeitet. Ihnen allen gebGhrt mein Dank. K.C. Literaturverzeichnis 1. G.H. Hardy and E.M. Wright, \"An Introduction to the Theory of Numbers\", Clarendon Press, Oxford, 1954. 2. H. Rademacher, \"Lectures on Elementary Number Theory\", Blaisdell Publishing Company, 1964. 3. A.E. Ingham, \"The Distribution of Prime Numbers\", Cambridge University Press, 1932. 4. H. Weyl, \"Ueber die Gleichverteilung von Zahlen mod. Eins\", Math. Annalen 77, 313-352 (1916). 5. C.L. Siegel, \"Ueber Gitterpunkte in Convexen K6rpern und ein damit zusammenh~ngendes Extremalproblem\", Acta Math. 65, 307-323 (1935). Inhaltsverzeichnis IQ Der Fundamentalsatz der elementaren Zahlentheorie. II. Kongruenzen. III. Die rationale Approximation einer irrationalen Zahl. Der Satz von Hurwitz IV. Quadratische Reste, und die Darstellbarkeit einer positiven ganzen Zahl als Summe von vier Quadraten. V~ Das quadratische Reziprozit~tsgesetz. VI. Zahlentheoretische Funktionen und Gitterpunkte. VII. Der Satz von Chebychev ~ber die Verteilung der Primzahlen. VIII. Die Weylsche \"Gleichverteilung von Zahlen mod I\", und der Satz von Kronecker. IX. Der Satz von Minkowski ~ber Gitterpunkte in konvexen Bereichen. X. Der Dirichletsche Satz von den Primzahlen in einer arithmetischen Progression.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52660084932881,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52660085915921,"sku":"NLS9783540036111","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540036111.jpg?v=1762264469"},{"product_id":"arithmetical-functions-book-komaravolu-chandrasekharan-9783642500282","title":"Arithmetical Functions","description":"The plan of this book had its inception in a course of lectures on arithmetical functions given by me in the summer of 1964 at the Forschungsinstitut fUr Mathematik of the Swiss Federal Institute of Technology, Zurich, at the invitation of Professor Beno Eckmann. My Introduction to Analytic Number Theory has appeared in the meanwhile, and this book may be looked upon as a sequel. It presupposes only a modicum of acquaintance with analysis and number theory. The arithmetical functions considered here are those associated with the distribution of prime numbers, as well as the partition function and the divisor function. Some of the problems posed by their asymptotic behaviour form the theme. They afford a glimpse of the variety of analytical methods used in the theory, and of the variety of problems that await solution. I owe a debt of gratitude to Professor Carl Ludwig Siegel, who has read the book in manuscript and given me the benefit of his criticism. I have improved the text in several places in response to his comments. I must thank Professor Raghavan Narasimhan for many stimulating discussions, and Mr. Henri Joris for the valuable assistance he has given me in checking the manuscript and correcting the proofs. K. Chandrasekharan July 1970 Contents Chapter I The prime number theorem and Selberg's method 1. Selberg's fonnula . . . . . . 1 2. A variant of Selberg's formula 6 12 3. Wirsing's inequality . . . . . 17 4. The prime number theorem. .","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52660541489425,"sku":"NLS9783642500282","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52761832980753,"sku":"NIN9783642500282","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642500282.jpg?v=1762265467"}],"url":"https:\/\/www.worldofbooks.com\/en-gb\/collections\/author-books-by-komaravolu-chandrasekharan.oembed","provider":"World of Books ","version":"1.0","type":"link"}