The theory of Hardy's Z-function:
Hardy's Z-function, related to the Riemann zeta-function ζ(s), was originally utilised by G. H. Hardy to show that ζ(s) has infinitely many zeros of the form ½+it. It is now amongst the most important functions of analytic number theory, and the Riemann hypothesis, that all complex zeros lie on...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2013
|
| Series: | Cambridge tracts in mathematics
196 |
| Subjects: | |
| Online Access: | DE-12 DE-92 DE-355 Volltext |
| Summary: | Hardy's Z-function, related to the Riemann zeta-function ζ(s), was originally utilised by G. H. Hardy to show that ζ(s) has infinitely many zeros of the form ½+it. It is now amongst the most important functions of analytic number theory, and the Riemann hypothesis, that all complex zeros lie on the line ½+it, is perhaps one of the best known and most important open problems in mathematics. Today Hardy's function has many applications; among others it is used for extensive calculations regarding the zeros of ζ(s). This comprehensive account covers many aspects of Z(t), including the distribution of its zeros, Gram points, moments and Mellin transforms. It features an extensive bibliography and end-of-chapter notes containing comments, remarks and references. The book also provides many open problems to stimulate readers interested in further research |
| Physical Description: | 1 Online-Ressource (xvii, 245 Seiten) |
| ISBN: | 9781139236973 |
| DOI: | 10.1017/CBO9781139236973 |
Staff View
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| contents | Definition of (s), Z(t) and basic notions -- Zeros on the critical line -- Selberg class of L-functions -- Approximate functional equations for k(s) -- Derivatives of Z(t) -- Gram points -- Moments of Hardy's function -- Primitive of Hardy's function -- Mellin transforms of powers of Z(t) -- Further results on Mk(s) and Zk(s) -- On some problems involving Hardy's function |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139236973 |
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| illustrated | Not Illustrated |
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| institution | BVB |
| isbn | 9781139236973 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350986 |
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| physical | 1 Online-Ressource (xvii, 245 Seiten) |
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| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Ivić, Aleksandar 1949-2020 Verfasser (DE-588)1037259343 aut The theory of Hardy's Z-function Aleksandar Ivić, Univerzitet u Beogradu, Serbia Cambridge Cambridge University Press 2013 1 Online-Ressource (xvii, 245 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 196 Definition of (s), Z(t) and basic notions -- Zeros on the critical line -- Selberg class of L-functions -- Approximate functional equations for k(s) -- Derivatives of Z(t) -- Gram points -- Moments of Hardy's function -- Primitive of Hardy's function -- Mellin transforms of powers of Z(t) -- Further results on Mk(s) and Zk(s) -- On some problems involving Hardy's function Hardy's Z-function, related to the Riemann zeta-function ζ(s), was originally utilised by G. H. Hardy to show that ζ(s) has infinitely many zeros of the form ½+it. It is now amongst the most important functions of analytic number theory, and the Riemann hypothesis, that all complex zeros lie on the line ½+it, is perhaps one of the best known and most important open problems in mathematics. Today Hardy's function has many applications; among others it is used for extensive calculations regarding the zeros of ζ(s). This comprehensive account covers many aspects of Z(t), including the distribution of its zeros, Gram points, moments and Mellin transforms. It features an extensive bibliography and end-of-chapter notes containing comments, remarks and references. The book also provides many open problems to stimulate readers interested in further research Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zetafunktion (DE-588)4190764-4 gnd rswk-swf Hardy-Klasse (DE-588)4159107-0 gnd rswk-swf Hardy-Klasse (DE-588)4159107-0 s Zetafunktion (DE-588)4190764-4 s Zahlentheorie (DE-588)4067277-3 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-107-02883-8 https://doi.org/10.1017/CBO9781139236973 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Ivić, Aleksandar 1949-2020 The theory of Hardy's Z-function Definition of (s), Z(t) and basic notions -- Zeros on the critical line -- Selberg class of L-functions -- Approximate functional equations for k(s) -- Derivatives of Z(t) -- Gram points -- Moments of Hardy's function -- Primitive of Hardy's function -- Mellin transforms of powers of Z(t) -- Further results on Mk(s) and Zk(s) -- On some problems involving Hardy's function Number theory Zahlentheorie (DE-588)4067277-3 gnd Zetafunktion (DE-588)4190764-4 gnd Hardy-Klasse (DE-588)4159107-0 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4190764-4 (DE-588)4159107-0 |
| title | The theory of Hardy's Z-function |
| title_auth | The theory of Hardy's Z-function |
| title_exact_search | The theory of Hardy's Z-function |
| title_full | The theory of Hardy's Z-function Aleksandar Ivić, Univerzitet u Beogradu, Serbia |
| title_fullStr | The theory of Hardy's Z-function Aleksandar Ivić, Univerzitet u Beogradu, Serbia |
| title_full_unstemmed | The theory of Hardy's Z-function Aleksandar Ivić, Univerzitet u Beogradu, Serbia |
| title_short | The theory of Hardy's Z-function |
| title_sort | the theory of hardy s z function |
| topic | Number theory Zahlentheorie (DE-588)4067277-3 gnd Zetafunktion (DE-588)4190764-4 gnd Hardy-Klasse (DE-588)4159107-0 gnd |
| topic_facet | Number theory Zahlentheorie Zetafunktion Hardy-Klasse |
| url | https://doi.org/10.1017/CBO9781139236973 |
| work_keys_str_mv | AT ivicaleksandar thetheoryofhardyszfunction |