An introduction to "G"-functions:
Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main object is the study of G-series, that is, power series y=aij=0 Ajxj with coefficients in an algebrai...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[1994]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 133 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main object is the study of G-series, that is, power series y=aij=0 Ajxj with coefficients in an algebraic number field K. These series satisfy a linear differential equation Ly=0 with LIK(x) [d/dx] and have non-zero radii of convergence for each imbedding of K into the complex numbers. They have the further property that the common denominators of the first s coefficients go to infinity geometrically with the index s. After presenting a review of valuation theory and elementary p-adic analysis together with an application to the congruence zeta function, this book offers a detailed study of the p-adic properties of formal power series solutions of linear differential equations. In particular, the p-adic radii of convergence and the p-adic growth of coefficients are studied. Recent work of Christol, Bombieri, André, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G -series is again a G -series. This book will be indispensable for those wishing to study the work of Bombieri and André on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) |
| Beschreibung: | 1 online resource |
| ISBN: | 9781400882540 |
| DOI: | 10.1515/9781400882540 |
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| 245 | 1 | 0 | |a An introduction to "G"-functions |c Bernard Dwork, Giovanni Gerotto, Francis J. Sullivan |
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| 490 | 1 | |a Annals of Mathematics Studies |v number 133 | |
| 500 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) | ||
| 520 | |a Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main object is the study of G-series, that is, power series y=aij=0 Ajxj with coefficients in an algebraic number field K. These series satisfy a linear differential equation Ly=0 with LIK(x) [d/dx] and have non-zero radii of convergence for each imbedding of K into the complex numbers. They have the further property that the common denominators of the first s coefficients go to infinity geometrically with the index s. After presenting a review of valuation theory and elementary p-adic analysis together with an application to the congruence zeta function, this book offers a detailed study of the p-adic properties of formal power series solutions of linear differential equations. In particular, the p-adic radii of convergence and the p-adic growth of coefficients are studied. Recent work of Christol, Bombieri, André, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G -series is again a G -series. This book will be indispensable for those wishing to study the work of Bombieri and André on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations | ||
| 546 | |a In English | ||
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Datensatz im Suchindex
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| author | Dwork, Bernard M. 1923-1998 Gerotto, Giovanni Sullivan, Francis J. |
| author_GND | (DE-588)117709654 |
| author_facet | Dwork, Bernard M. 1923-1998 Gerotto, Giovanni Sullivan, Francis J. |
| author_role | aut aut aut |
| author_sort | Dwork, Bernard M. 1923-1998 |
| author_variant | b m d bm bmd g g gg f j s fj fjs |
| building | Verbundindex |
| bvnumber | BV043712514 |
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| dewey-full | 515/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.55 |
| dewey-search | 515/.55 |
| dewey-sort | 3515 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400882540 |
| format | Electronic eBook |
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| spelling | Dwork, Bernard M. 1923-1998 (DE-588)117709654 aut An introduction to "G"-functions Bernard Dwork, Giovanni Gerotto, Francis J. Sullivan Princeton, NJ Princeton University Press [1994] © 1994 1 online resource txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 133 Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main object is the study of G-series, that is, power series y=aij=0 Ajxj with coefficients in an algebraic number field K. These series satisfy a linear differential equation Ly=0 with LIK(x) [d/dx] and have non-zero radii of convergence for each imbedding of K into the complex numbers. They have the further property that the common denominators of the first s coefficients go to infinity geometrically with the index s. After presenting a review of valuation theory and elementary p-adic analysis together with an application to the congruence zeta function, this book offers a detailed study of the p-adic properties of formal power series solutions of linear differential equations. In particular, the p-adic radii of convergence and the p-adic growth of coefficients are studied. Recent work of Christol, Bombieri, André, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G -series is again a G -series. This book will be indispensable for those wishing to study the work of Bombieri and André on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations In English H-functions p-adic analysis G-Funktion (DE-588)4210136-0 gnd rswk-swf G-Funktion (DE-588)4210136-0 s 1\p DE-604 Gerotto, Giovanni aut Sullivan, Francis J. aut Erscheint auch als Druck-Ausgabe 978-0-691-03681-6 Annals of Mathematics Studies number 133 (DE-604)BV040389493 133 https://doi.org/10.1515/9781400882540?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dwork, Bernard M. 1923-1998 Gerotto, Giovanni Sullivan, Francis J. An introduction to "G"-functions Annals of Mathematics Studies H-functions p-adic analysis G-Funktion (DE-588)4210136-0 gnd |
| subject_GND | (DE-588)4210136-0 |
| title | An introduction to "G"-functions |
| title_auth | An introduction to "G"-functions |
| title_exact_search | An introduction to "G"-functions |
| title_full | An introduction to "G"-functions Bernard Dwork, Giovanni Gerotto, Francis J. Sullivan |
| title_fullStr | An introduction to "G"-functions Bernard Dwork, Giovanni Gerotto, Francis J. Sullivan |
| title_full_unstemmed | An introduction to "G"-functions Bernard Dwork, Giovanni Gerotto, Francis J. Sullivan |
| title_short | An introduction to "G"-functions |
| title_sort | an introduction to g functions |
| topic | H-functions p-adic analysis G-Funktion (DE-588)4210136-0 gnd |
| topic_facet | H-functions p-adic analysis G-Funktion |
| url | https://doi.org/10.1515/9781400882540?locatt=mode:legacy |
| volume_link | (DE-604)BV040389493 |
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