內容簡介
本書是數論領域的一部傳世名著,成書於作者在牛津大學、劍橋大學等學校授課的講義。書中從各個不同角度對數論進行了闡述,內容包括素數、無理數、同餘、費馬定理、連分數、不定式、二次域、算術函式、分化等。新版修訂了每章末的註解,簡要介紹了數論最新的發展;增加了一章講述橢圓曲線,這是數論中最重要的突破之一。還列出進一步閱讀的文獻。
本書適合數學專業本科生、研究生和教師用作教材或參考書,也適合對數論感興趣的專業人士閱讀參考。
作者簡介
Hardy(1877-1947)20世紀上半葉享有世界聲譽的數學大師,是英國數學界和英國分析學派的領袖,對數論和分析學的發展有巨大的貢獻和重大的影響,除了自己的研究工作之外,他還培養和指導了眾多數學大家,包括印度數學奇才拉馬努金和我國數學家華羅庚。
圖書目錄
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
CONTINUED FRACTIONS
APPROXIMATION OF IRRATIONALS BY RATIONALS
THE FUNDAMENIAL THEOREM OF ARITHMETIC INk
SOME DIOPHANTINE EQUATIONS
OUADRATIC FIELDS (1)
OUADRATIC FIELDS (2)
THEarithmeticalFUNCTIONS
GENERATING FUNCTIONS OF ARITHMETICAL FUNCTIONS
THE ORDER OF MAGNITUDE OF ARITHMETICAL FUNCTIONS
PARTITIONS361
THE REPRESENTATION OF A NUMBER BY TWO OR FOUR SQUARES
REPRESENTATION BY CUBES AND HIGHER POWERS
THE SERIES OF PRIMES(3)
KRONECKER'S THEOREM
GEOMETRY OF NUMBERS
ELLIPTIC CURVES
APPENDIX
A LIST OF BOOKS
INDEX OF SPECIAL SYMBOLS AND WORDS
INDEX OF NAMES
GENERAL INDEX