Arithmetical functions: an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties
The aim of this book is to characterize certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. The authors achieve this goal by considering convolutions of arithmetical functions, elementary mea...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1994
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| Schriftenreihe: | London Mathematical Society lecture note series
184 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | The aim of this book is to characterize certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. The authors achieve this goal by considering convolutions of arithmetical functions, elementary mean-value theorems, and properties of related multiplicative functions. They also prove the mean-value theorems of Wirsing and Halász and study the pointwise convergence of the Ramanujan expansion. Finally, some applications to power series with multiplicative coefficients are included, along with exercises and an extensive bibliography |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xix, 367 pages) |
| ISBN: | 9781107359963 |
| DOI: | 10.1017/CBO9781107359963 |
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| 245 | 1 | 0 | |a Arithmetical functions |b an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties |c Wolfgang Schwarz, Jürgen Spilker |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 520 | |a The aim of this book is to characterize certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. The authors achieve this goal by considering convolutions of arithmetical functions, elementary mean-value theorems, and properties of related multiplicative functions. They also prove the mean-value theorems of Wirsing and Halász and study the pointwise convergence of the Ramanujan expansion. Finally, some applications to power series with multiplicative coefficients are included, along with exercises and an extensive bibliography | ||
| 650 | 4 | |a Arithmetic functions | |
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| 650 | 4 | |a Mean value theorems (Calculus) | |
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Datensatz im Suchindex
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| author | Schwarz, Wolfgang 1934- |
| author_facet | Schwarz, Wolfgang 1934- |
| author_role | aut |
| author_sort | Schwarz, Wolfgang 1934- |
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| bvnumber | BV043942015 |
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| ctrlnum | (ZDB-20-CBO)CR9781107359963 (OCoLC)890461310 (DE-599)BVBBV043942015 |
| dewey-full | 512/.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.73 |
| dewey-search | 512/.73 |
| dewey-sort | 3512 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781107359963 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9781107359963 |
| language | English |
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| publishDate | 1994 |
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| spelling | Schwarz, Wolfgang 1934- Verfasser aut Arithmetical functions an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties Wolfgang Schwarz, Jürgen Spilker Cambridge Cambridge University Press 1994 1 online resource (xix, 367 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 184 Title from publisher's bibliographic system (viewed on 05 Oct 2015) The aim of this book is to characterize certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. The authors achieve this goal by considering convolutions of arithmetical functions, elementary mean-value theorems, and properties of related multiplicative functions. They also prove the mean-value theorems of Wirsing and Halász and study the pointwise convergence of the Ramanujan expansion. Finally, some applications to power series with multiplicative coefficients are included, along with exercises and an extensive bibliography Arithmetic functions Number theory Mean value theorems (Calculus) Arithmetische Funktion (DE-588)4368429-4 gnd rswk-swf Zahlentheoretische Funktion (DE-588)4067276-1 gnd rswk-swf Zahlentheoretische Funktion (DE-588)4067276-1 s 1\p DE-604 Arithmetische Funktion (DE-588)4368429-4 s 2\p DE-604 Spilker, Jürgen Sonstige oth Erscheint auch als Druckausgabe 978-0-521-42725-8 https://doi.org/10.1017/CBO9781107359963 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Schwarz, Wolfgang 1934- Arithmetical functions an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties Arithmetic functions Number theory Mean value theorems (Calculus) Arithmetische Funktion (DE-588)4368429-4 gnd Zahlentheoretische Funktion (DE-588)4067276-1 gnd |
| subject_GND | (DE-588)4368429-4 (DE-588)4067276-1 |
| title | Arithmetical functions an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties |
| title_auth | Arithmetical functions an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties |
| title_exact_search | Arithmetical functions an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties |
| title_full | Arithmetical functions an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties Wolfgang Schwarz, Jürgen Spilker |
| title_fullStr | Arithmetical functions an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties Wolfgang Schwarz, Jürgen Spilker |
| title_full_unstemmed | Arithmetical functions an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties Wolfgang Schwarz, Jürgen Spilker |
| title_short | Arithmetical functions |
| title_sort | arithmetical functions an introduction to elementary and analytic properties of arithmetic functions and to some of their almost periodic properties |
| title_sub | an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties |
| topic | Arithmetic functions Number theory Mean value theorems (Calculus) Arithmetische Funktion (DE-588)4368429-4 gnd Zahlentheoretische Funktion (DE-588)4067276-1 gnd |
| topic_facet | Arithmetic functions Number theory Mean value theorems (Calculus) Arithmetische Funktion Zahlentheoretische Funktion |
| url | https://doi.org/10.1017/CBO9781107359963 |
| work_keys_str_mv | AT schwarzwolfgang arithmeticalfunctionsanintroductiontoelementaryandanalyticpropertiesofarithmeticfunctionsandtosomeoftheiralmostperiodicproperties AT spilkerjurgen arithmeticalfunctionsanintroductiontoelementaryandanalyticpropertiesofarithmeticfunctionsandtosomeoftheiralmostperiodicproperties |