哈代數(shù)論

前言

　　This sixth edition contains a considerable expansion of the end-of-chapternotes. There have been many exciting developments since these were lastrevised， which are now described in the notes. It is hoped that these willprovide an avenue leading the interested reader towards current researchareas. The notes for some chapters were written with the generous help ofother authorities. Professor D. Masser updated the material on Chapters4 and 11， while Professor G.E. Andrews did the same for Chapter 19. Asubstantial amount of new material was added to the notes for Chapter 21by Professor T.D. Wooley， and a similar review of the notes for Chapter 24was undertaken by Professor R. Hans-Gill. We are naturally very gratefulto all of them for their assistance.　　In addition， we have added a substantial new chapter， dealing with ellip-tic curves. This subject， which was not mentioned in earlier editions， hascome to be such a central topic in the theory of numbers that it was feltto deserve a full treatment. The material is naturally connected with theoriginal chapter on Dlophantlne Equations.　　Finally， we have corrected a significant number of misprints in thefifth edition. A large number of correspondents reported typographical ormathematical errors， and we thank everyone who contributed in this way.　　The proposal to produce this new edition originally came from ProfessorsJohn Maitland Wright and John Coates. We are very grateful for theirenthusiastic support.

內(nèi)容概要

　　本書是數(shù)論領(lǐng)域的一部傳世名著，成書于作者在牛津大學(xué)、劍橋大學(xué)等學(xué)校授課的講義。書中從各個(gè)不同角度對(duì)數(shù)論進(jìn)行了闡述，內(nèi)容包括素?cái)?shù)、無理數(shù)、同余、費(fèi)馬定理、連分?jǐn)?shù)、不定式、二次域、算術(shù)函數(shù)、分化等。新版修訂了每章末的注解，簡(jiǎn)要介紹了數(shù)論最新的發(fā)展；增加了一章講述橢圓曲線，這是數(shù)論中最重要的突破之一。還列出進(jìn)一步閱讀的文獻(xiàn)。　　本書適合數(shù)學(xué)專業(yè)本科生、研究生和教師用作教材或參考書，也適合對(duì)數(shù)論感興趣的專業(yè)人士閱讀參考。

作者簡(jiǎn)介

　　G.H.Hardy（1877-1947）20世紀(jì)上半葉享有世界聲譽(yù)的數(shù)學(xué)大師，是英國(guó)數(shù)學(xué)界和英國(guó)分析學(xué)派的領(lǐng)袖，對(duì)數(shù)論和分析學(xué)的發(fā)展有巨大的貢獻(xiàn)和重大的影響，除了自己的研究工作之外，他還培養(yǎng)和指導(dǎo)了眾多數(shù)學(xué)大家，包括印度數(shù)學(xué)奇才拉馬努金和我國(guó)數(shù)學(xué)家華羅庚。

書籍目錄

I. THE SERIES OF PRIMES （1）　II. THE SERIES OF PRIMES （2）　III. FAREY SERIES AND A THEOREM OF MINKOWSKI　IV. IRRATIONAL NUMBERS　V. CONGRUENCES AND RESIDUES　VI. FFRMAT's THEOREM AND ITS CONSEOUENCES　VII. GENERAL PROPERTIES OF CONGRUENCES　VIII. CONGRUENCES TO COMPOSITE MODULI　IX. THE REPRESENTATION OF NUMBERS BY DECIMALS　X. CONTINUED FRACTIONS　XI. APPROXIMATION OF IRRATIONALS BY RATIONALS　XlI. THE FUNDAMENIAL THEOREM OF ARITHMETIC INk（1）, k（i）, AND k（O）　XIII. SOME DIOPHANTINE EQUATIONS　XIV. OUADRATIC FIELDS （1）　XV. OUADRATIC FIELDS （2）　XVI. THE ARITHMETICAL FUNCTIONS Ф（n）,μ（n）, d（n）, σ（n）, r（n）   XVII. GENERATING FUNCTIONS OF ARITHMETICAL FUNCTIONS　XVIII. THE ORDER OF MAGNITUDE OF ARITHMETICAL FUNCTIONS　XIX. PARTITIONS　361XX. THE REPRESENTATION OF A NUMBER BY TWO OR FOUR SQUARES　XXI. REPRESENTATION BY CUBES AND HIGHER POWERS　XXII. THE SERIES OF PRIMES（3）　XXIII. KRONECKER'S THEOREM　XXIV. GEOMETRY OF NUMBERS　XXV. ELLIPTIC CURVES　APPENDIX　A LIST OF BOOKS　INDEX OF SPECIAL SYMBOLS AND WORDS　INDEX OF NAMES　GENERAL INDEX　

媒體關(guān)注與評(píng)論

　　“這本引人入勝的書對(duì)這一學(xué)科進(jìn)行了生動(dòng)、詳盡的敘述，而且沒有用到太多高深的理論。”　　——Mathematical Gazette（數(shù)學(xué)公報(bào)）　　“……一本非常重要的著作……它一定能繼續(xù)保持長(zhǎng)久、旺盛的生命力……”　　——Mathematical Reviews（數(shù)學(xué)評(píng)論）

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