On Dwork’s (Record no. 128023)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04036nam a22004813i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC4908279 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729131328.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2017 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470436353 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470423001 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC4908279 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL4908279 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr11409825 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)968205459 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA564.D453 2017 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.74 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Delaygue, E. |
| 245 10 - TITLE STATEMENT | |
| Title | On Dwork’s |
| Name of part/section of a work | |
| -- | Adic Formal Congruences Theorem and Hypergeometric Mirror Maps. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2017. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2016. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (106 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society ; |
| Volume/sequential designation | v.246 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Statements of the main results -- 2.1. -integrality of _{ , } -- 2.2. Generalizations of Dwork's congruence -- 2.3. -Integrality of _{ , } -- 2.4. -Integrality of _{ , } -- Chapter 3. Structure of the paper -- Chapter 4. Comments on the main results, comparison with previous results and open questions -- 4.1. Comments on Theorem 3, Theorem 4 and on the hypothesis _{ , } -- 4.2. Comparison with previous results -- 4.3. Open questions -- 4.4. A corrected version of a lemma of Lang -- Chapter 5. The -adic valuation of Pochhammer symbols -- 5.1. Christol's criterion for the -integrality of _{ , } -- 5.2. Dwork's map _{ } -- 5.3. Analogues of Landau functions -- Chapter 6. Proof of Theorem 4 -- Chapter 7. Formal congruences -- 7.1. Proof of Theorem 30 -- Chapter 8. Proof of Theorem 6 -- 8.1. Algebras of functions taking values into ℤ_{ } -- 8.2. Proof of Theorem 6 -- Chapter 9. Proof of Theorem 9 -- Chapter 10. Proof of Theorem 12 -- 10.1. A -adic reformulation of Theorem 12 -- Chapter 11. Proof of Theorem 8 -- 11.1. Proof of Assertion ( ) of Theorem 8 -- 11.2. Proof of Assertion ( ) of Theorem 8 -- 11.3. Last step in the proof of Theorem 8 -- Chapter 12. Proof of Theorem 10 -- Chapter 13. Proof of Corollary 14 -- Bibliography -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | Using Dwork's theory, the authors prove a broad generalization of his famous p-adic formal congruences theorem. This enables them to prove certain p-adic congruences for the generalized hypergeometric series with rational parameters; in particular, they hold for any prime number p and not only for almost all primes. Furthermore, using Christol's functions, the authors provide an explicit formula for the "Eisenstein constant" of any hypergeometric series with rational parameters. As an application of these results, the authors obtain an arithmetic statement "on average" of a new type concerning the integrality of Taylor coefficients of the associated mirror maps. It contains all the similar univariate integrality results in the literature, with the exception of certain refinements that hold only in very particular cases. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Geometry, Algebraic. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Rivoal, T. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Roques, J. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Delaygue, E. |
| Title | On Dwork’s |
| -- | |
| -- | Adic Formal Congruences Theorem and Hypergeometric Mirror Maps |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2017 |
| International Standard Book Number | 9781470423001 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4908279">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4908279</a> |
| Public note | Click to View |
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