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Lieferstatus:	i.d.R. innert 14-24 Tagen versandfertig
Veröffentlichung:	August 2023
Genre:	Schulbücher
ISBN:	9789811279317
EAN-Code:	9789811279317
Verlag:	Wspc
Einband:	Gebunden
Sprache:	English
Dimensionen:	H 235 mm / B 157 mm / D 15 mm
Gewicht:	439 gr
Seiten:	192
Zus. Info:	HC gerader Rücken kaschiert
Bewertung:	Titel bewerten / Meinung schreiben

Inhalt:

There is no surprise that arithmetic properties of integral ("whole") numbers are controlled by analytic functions of complex variable. At the same time, the values of analytic functions themselves happen to be interesting numbers, for which we often seek explicit expressions in terms of other "better known" numbers or try to prove that no such exist. This natural symbiosis of number theory and analysis is centuries old but keeps enjoying new results, ideas and methods. The present book takes a semi-systematic review of analytic achievements in number theory ranging from classical themes about primes, continued fractions, transcendence of ¿ and resolution of Hilbert's seventh problem to some recent developments on the irrationality of the values of Riemann's zeta function, sizes of non-cyclotomic algebraic integers and applications of hypergeometric functions to integer congruences. Our principal goal is to present a variety of different analytic techniques that are used in number theory, at a reasonably accessible - almost popular - level, so that the materials from this book can suit for teaching a graduate course on the topic or for a self-study. Exercises included are of varying difficulty and of varying distribution within the book (some chapters get more than other); they not only help the reader to consolidate their understanding of the material but also suggest directions for further study and investigation. Furthermore, the end of each chapter features brief notes about relevant developments of the themes discussed.