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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¿Fänle¿b 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.
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¿Fänle¿b 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.
Olivier Ramaré is a Research Director at Aix Marseille Université in Marseille, France. He is a prolific researcher with a focus on sieve theory, prime numbers, the Möbius function, L-series, and more.
Offers a unique exploration of analytic number theory that focuses on proving explicit bounds in cases suited to versatile tools
Emphasizes a methodological approach to the material with several different pathways to proceed
Promotes an active learning style with nearly 300 exercises appearing throughout
| Erscheinungsjahr: | 2022 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: |
xxii
338 S. 2 s/w Illustr. 13 farbige Illustr. 338 p. 15 illus. 13 illus. in color. |
| ISBN-13: | 9783030731687 |
| ISBN-10: | 3030731685 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Ramaré, Olivier |
| Auflage: | 1st edition 2022 |
| Hersteller: |
Springer Nature Switzerland
Springer International Publishing Springer International Publishing AG |
| Verantwortliche Person für die EU: | Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com |
| Maße: | 241 x 160 x 24 mm |
| Von/Mit: | Olivier Ramaré |
| Erscheinungsdatum: | 04.03.2022 |
| Gewicht: | 0,771 kg |
Olivier Ramaré is a Research Director at Aix Marseille Université in Marseille, France. He is a prolific researcher with a focus on sieve theory, prime numbers, the Möbius function, L-series, and more.
Offers a unique exploration of analytic number theory that focuses on proving explicit bounds in cases suited to versatile tools
Emphasizes a methodological approach to the material with several different pathways to proceed
Promotes an active learning style with nearly 300 exercises appearing throughout
| Erscheinungsjahr: | 2022 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: |
xxii
338 S. 2 s/w Illustr. 13 farbige Illustr. 338 p. 15 illus. 13 illus. in color. |
| ISBN-13: | 9783030731687 |
| ISBN-10: | 3030731685 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Ramaré, Olivier |
| Auflage: | 1st edition 2022 |
| Hersteller: |
Springer Nature Switzerland
Springer International Publishing Springer International Publishing AG |
| Verantwortliche Person für die EU: | Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com |
| Maße: | 241 x 160 x 24 mm |
| Von/Mit: | Olivier Ramaré |
| Erscheinungsdatum: | 04.03.2022 |
| Gewicht: | 0,771 kg |
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