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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Arithmetik & Algebra Excursions in Multiplicative Number Theory
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Beschreibung
This textbook offers a unique exploration of analytic number theory that is focused on explicit and realistic numerical bounds. By giving precise proofs in simplified settings, the author strategically builds practical tools and insights for exploring the behavior of arithmetical functions. An active learning style is encouraged across nearly three hundred exercises, making this an indispensable… resource for both students and instructors. Designed to allow readers several different pathways to progress from basic notions to active areas of research, the book begins with a study of arithmetic functions and notions of arithmetical interest. From here, several guided “walks” invite readers to continue, offering explorations along three broad themes: the convolution method, the Levin–Faĭnleĭb theorem, and the Mellin transform. Having followed any one of the walks, readers will arrive at “higher ground”, where they will find opportunities for extensions and applications, such asthe Selberg formula, Brun’s sieve, and the Large Sieve Inequality. Methodology is emphasized throughout, with frequent opportunities to explore numerically using computer algebra packages Pari/GP and Sage. Excursions in Multiplicative Number Theory is ideal for graduate students and upper-level undergraduate students who are familiar with the fundamentals of analytic number theory. It will also appeal to researchers in mathematics and engineering interested in experimental techniques in this active area. 58,84 €
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Technische Daten
Erscheinungsdatum
05.03.2023
Sprache
Englisch
EAN
9783030731717
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Birkhäuser Advanced Texts Basler Lehrbücher
Sonderedition
Nein
Autor
Olivier Ramaré
Seitenanzahl
338
Einbandart
Broschiert
Schlagwörter
Analytic number theory, Prime number theory, Euler products, Multiplicative functions number theory, Multiplicative arithmetic functions, Divisor functions, Convolution of divisor functions, Riemann zeta function, Dirichlet series, Unitary convolution, Möbius inversion, Legendre symbol, Convolutions method number theory, Levin Fainleib theorem, Mellin transform, Large sieve number theory, Exponential sums with arithmetical coefficients, Selberg formula
Thema-Inhalt
PBH - Zahlentheorie
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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