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Nathanson for his excellent translation and for much assistance in correcting errors in the original text. I express my deep gratitude to Professor Melvyn B. I hope that the English edition will be used in the same ways. 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. Nathanson Introduction to the English Edition It gives me great pleasure that Springer-Verlag is publishing an English trans lation of my book.
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For the English edition, the author has considerably rewritten Chapter I, and has corrected various typographical and other minor errors throughout the the text. This English translation of Karatsuba's Basic Analytic Number Theory follows closely the second Russian edition, published in Moscow in 1983. In particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.
BASIC NUMBER THEORY PROBLEMS SERIES
The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares. Elementary ideas about groups and rings are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra. Publisher: Springer Science & Business MediaĪn undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples.