Brandt Matrices and Theta Series over Global Function Fields. (Record no. 124845)
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| fixed length control field | 04121nam a22004933i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC4832024 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729131156.0 |
| 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 | 240724s2015 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470425012 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470414191 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC4832024 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL4832024 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr11367309 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)917874773 |
| 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 | QA196.B736 2015 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.70000000000005 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Chuang, Chih-Yun. |
| 245 10 - TITLE STATEMENT | |
| Title | Brandt Matrices and Theta Series over Global Function Fields. |
| 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 | 2015. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2015. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (76 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.237 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Brandt matrices and definite Shimura curves -- 1. Basic setting -- 2. Definite quaternion algebra over function fields -- 3. Brandt matrices -- 4. Definite Shimura curves -- 4.1. Hecke correspondences -- 4.2. Gross height pairing -- Chapter 3. The basis problem for Drinfeld type automorphic forms -- 1. Weil representation -- 1.1. Weil representation of \SL₂× ( ) -- 1.2. Test functions from arithmetic data -- 2. Theta series -- 3. Drinfeld type automorphic forms and Hecke operators -- 3.1. Fourier coefficients of theta series -- 4. The Hecke module homomorphism Φ -- 4.1. Changing levels -- 5. Construction of Drinfeld type newforms -- 6. The basis problem -- Chapter 4. Metaplectic forms and Shintani-type correspondence -- 1. Metaplectic forms -- 1.1. Metaplectic group -- 1.2. Weil representation and theta series from pure quaternions -- 1.3. Fourier coefficients of metaplectic theta series -- 2. Hecke operators and Shintani-type correspondence -- 3. Pure quaternions and Brandt matrices -- Chapter 5. Trace formula of Brandt matrices -- 1. Optimal embeddings -- 1.1. Local optimal embeddings -- 2. Trace formula -- Bibliography -- Symbols -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | The aim of this article is to give a complete account of the Eichler-Brandt theory over function fields and the basis problem for Drinfeld type automorphic forms. Given arbitrary function field k together with a fixed place \infty, the authors construct a family of theta series from the norm forms of "definite" quaternion algebras, and establish an explicit Hecke-module homomorphism from the Picard group of an associated definite Shimura curve to a space of Drinfeld type automorphic forms. The "compatibility" of these homomorphisms with different square-free levels is also examined. These Hecke-equivariant maps lead to a nice description of the subspace generated by the authors' theta series, and thereby contributes to the so-called basis problem. Restricting the norm forms to pure quaternions, the authors obtain another family of theta series which are automorphic functions on the metaplectic group, and this results in a Shintani-type correspondence between Drinfeld type forms and metaplectic forms. |
| 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 | Matrices. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Lee, Ting-Fang. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Wei, Fu-Tsun. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Yu, Jing. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Chuang, Chih-Yun |
| Title | Brandt Matrices and Theta Series over Global Function Fields |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2015 |
| International Standard Book Number | 9781470414191 |
| 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=4832024">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4832024</a> |
| Public note | Click to View |
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