The Lerch Zeta-function:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2002
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The Lerch zeta-function is the first monograph on this topic, which is a generalization of the classic Riemann, and Hurwitz zeta-functions. Although analytic results have been presented previously in various monographs on zeta-functions, this is the first book containing both analytic and probability theory of Lerch zeta-functions. The book starts with classical analytical theory (Euler gamma-functions, functional equation, mean square). The majority of the presented results are new: on approximate functional equations and its applications and on zero distribution (zero-free regions, number of nontrivial zeros etc). Special attention is given to limit theorems in the sense of the weak convergence of probability measures for the Lerch zeta-function. From limit theorems in the space of analytic functions the universitality and functional independence is derived. In this respect the book continues the research of the first author presented in the monograph Limit Theorems for the Riemann zeta-function. This book will be useful to researchers and graduate students working in analytic and probabilistic number theory, and can also be used as a textbook for postgraduate students |
| Beschreibung: | 1 Online-Ressource (VIII, 189 p) |
| ISBN: | 9789401764018 9789048161683 |
| DOI: | 10.1007/978-94-017-6401-8 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042424334 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2002 |||| o||u| ||||||eng d | ||
| 020 | |a 9789401764018 |c Online |9 978-94-017-6401-8 | ||
| 020 | |a 9789048161683 |c Print |9 978-90-481-6168-3 | ||
| 024 | 7 | |a 10.1007/978-94-017-6401-8 |2 doi | |
| 035 | |a (OCoLC)879622400 | ||
| 035 | |a (DE-599)BVBBV042424334 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 512.7 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Laurinčikas, Antanas |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The Lerch Zeta-function |c by Antanas Laurinčikas, Ramūnas Garunkštis |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 2002 | |
| 300 | |a 1 Online-Ressource (VIII, 189 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 500 | |a The Lerch zeta-function is the first monograph on this topic, which is a generalization of the classic Riemann, and Hurwitz zeta-functions. Although analytic results have been presented previously in various monographs on zeta-functions, this is the first book containing both analytic and probability theory of Lerch zeta-functions. The book starts with classical analytical theory (Euler gamma-functions, functional equation, mean square). The majority of the presented results are new: on approximate functional equations and its applications and on zero distribution (zero-free regions, number of nontrivial zeros etc). Special attention is given to limit theorems in the sense of the weak convergence of probability measures for the Lerch zeta-function. From limit theorems in the space of analytic functions the universitality and functional independence is derived. In this respect the book continues the research of the first author presented in the monograph Limit Theorems for the Riemann zeta-function. This book will be useful to researchers and graduate students working in analytic and probabilistic number theory, and can also be used as a textbook for postgraduate students | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Functional equations | |
| 650 | 4 | |a Functions of complex variables | |
| 650 | 4 | |a Functions, special | |
| 650 | 4 | |a Number theory | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Number Theory | |
| 650 | 4 | |a Functions of a Complex Variable | |
| 650 | 4 | |a Special Functions | |
| 650 | 4 | |a Probability Theory and Stochastic Processes | |
| 650 | 4 | |a Difference and Functional Equations | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Zetafunktion |0 (DE-588)4190764-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Zetafunktion |0 (DE-588)4190764-4 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Garunkštis, Ramūnas |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-94-017-6401-8 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027859751 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153101161070592 |
|---|---|
| any_adam_object | |
| author | Laurinčikas, Antanas |
| author_facet | Laurinčikas, Antanas |
| author_role | aut |
| author_sort | Laurinčikas, Antanas |
| author_variant | a l al |
| building | Verbundindex |
| bvnumber | BV042424334 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)879622400 (DE-599)BVBBV042424334 |
| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| 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 | 10.1007/978-94-017-6401-8 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03070nmm a2200553zc 4500</leader><controlfield tag="001">BV042424334</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2002 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401764018</subfield><subfield code="c">Online</subfield><subfield code="9">978-94-017-6401-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789048161683</subfield><subfield code="c">Print</subfield><subfield code="9">978-90-481-6168-3</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-94-017-6401-8</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)879622400</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042424334</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.7</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Laurinčikas, Antanas</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The Lerch Zeta-function</subfield><subfield code="c">by Antanas Laurinčikas, Ramūnas Garunkštis</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht</subfield><subfield code="b">Springer Netherlands</subfield><subfield code="c">2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (VIII, 189 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The Lerch zeta-function is the first monograph on this topic, which is a generalization of the classic Riemann, and Hurwitz zeta-functions. Although analytic results have been presented previously in various monographs on zeta-functions, this is the first book containing both analytic and probability theory of Lerch zeta-functions. The book starts with classical analytical theory (Euler gamma-functions, functional equation, mean square). The majority of the presented results are new: on approximate functional equations and its applications and on zero distribution (zero-free regions, number of nontrivial zeros etc). Special attention is given to limit theorems in the sense of the weak convergence of probability measures for the Lerch zeta-function. From limit theorems in the space of analytic functions the universitality and functional independence is derived. In this respect the book continues the research of the first author presented in the monograph Limit Theorems for the Riemann zeta-function. This book will be useful to researchers and graduate students working in analytic and probabilistic number theory, and can also be used as a textbook for postgraduate students</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functions of complex variables</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functions, special</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Distribution (Probability theory)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functions of a Complex Variable</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Special Functions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Probability Theory and Stochastic Processes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Difference and Functional Equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zetafunktion</subfield><subfield code="0">(DE-588)4190764-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Zetafunktion</subfield><subfield code="0">(DE-588)4190764-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Garunkštis, Ramūnas</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-94-017-6401-8</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027859751</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042424334 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401764018 9789048161683 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859751 |
| oclc_num | 879622400 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (VIII, 189 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer Netherlands |
| record_format | marc |
| spelling | Laurinčikas, Antanas Verfasser aut The Lerch Zeta-function by Antanas Laurinčikas, Ramūnas Garunkštis Dordrecht Springer Netherlands 2002 1 Online-Ressource (VIII, 189 p) txt rdacontent c rdamedia cr rdacarrier The Lerch zeta-function is the first monograph on this topic, which is a generalization of the classic Riemann, and Hurwitz zeta-functions. Although analytic results have been presented previously in various monographs on zeta-functions, this is the first book containing both analytic and probability theory of Lerch zeta-functions. The book starts with classical analytical theory (Euler gamma-functions, functional equation, mean square). The majority of the presented results are new: on approximate functional equations and its applications and on zero distribution (zero-free regions, number of nontrivial zeros etc). Special attention is given to limit theorems in the sense of the weak convergence of probability measures for the Lerch zeta-function. From limit theorems in the space of analytic functions the universitality and functional independence is derived. In this respect the book continues the research of the first author presented in the monograph Limit Theorems for the Riemann zeta-function. This book will be useful to researchers and graduate students working in analytic and probabilistic number theory, and can also be used as a textbook for postgraduate students Mathematics Functional equations Functions of complex variables Functions, special Number theory Distribution (Probability theory) Number Theory Functions of a Complex Variable Special Functions Probability Theory and Stochastic Processes Difference and Functional Equations Mathematik Zetafunktion (DE-588)4190764-4 gnd rswk-swf Zetafunktion (DE-588)4190764-4 s 1\p DE-604 Garunkštis, Ramūnas Sonstige oth https://doi.org/10.1007/978-94-017-6401-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Laurinčikas, Antanas The Lerch Zeta-function Mathematics Functional equations Functions of complex variables Functions, special Number theory Distribution (Probability theory) Number Theory Functions of a Complex Variable Special Functions Probability Theory and Stochastic Processes Difference and Functional Equations Mathematik Zetafunktion (DE-588)4190764-4 gnd |
| subject_GND | (DE-588)4190764-4 |
| title | The Lerch Zeta-function |
| title_auth | The Lerch Zeta-function |
| title_exact_search | The Lerch Zeta-function |
| title_full | The Lerch Zeta-function by Antanas Laurinčikas, Ramūnas Garunkštis |
| title_fullStr | The Lerch Zeta-function by Antanas Laurinčikas, Ramūnas Garunkštis |
| title_full_unstemmed | The Lerch Zeta-function by Antanas Laurinčikas, Ramūnas Garunkštis |
| title_short | The Lerch Zeta-function |
| title_sort | the lerch zeta function |
| topic | Mathematics Functional equations Functions of complex variables Functions, special Number theory Distribution (Probability theory) Number Theory Functions of a Complex Variable Special Functions Probability Theory and Stochastic Processes Difference and Functional Equations Mathematik Zetafunktion (DE-588)4190764-4 gnd |
| topic_facet | Mathematics Functional equations Functions of complex variables Functions, special Number theory Distribution (Probability theory) Number Theory Functions of a Complex Variable Special Functions Probability Theory and Stochastic Processes Difference and Functional Equations Mathematik Zetafunktion |
| url | https://doi.org/10.1007/978-94-017-6401-8 |
| work_keys_str_mv | AT laurincikasantanas thelerchzetafunction AT garunkstisramunas thelerchzetafunction |