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."
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