Algebraic relations among Goss’s zeta values on elliptic curves
In 2007 Chang and Yu determined all the algebraic relations among Goss’s zeta values for $A=\mathbb F_q[\theta ]$ , also known as the Carlitz zeta values. Goss raised the problem of determining all algebraic relations among Goss’s zeta values at positive integers for a general base ring A, but...
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2023-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509423000944/type/journal_article |
| _version_ | 1827799387259011072 |
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| author | Nathan Green Tuan Ngo Dac |
| author_facet | Nathan Green Tuan Ngo Dac |
| author_sort | Nathan Green |
| collection | DOAJ |
| description | In 2007 Chang and Yu determined all the algebraic relations among Goss’s zeta values for
$A=\mathbb F_q[\theta ]$
, also known as the Carlitz zeta values. Goss raised the problem of determining all algebraic relations among Goss’s zeta values at positive integers for a general base ring A, but very little is known. In this paper, we develop a general method, and we determine all algebraic relations among Goss’s zeta values for the base ring A which is the coordinate ring of an elliptic curve defined over
$\mathbb F_q$
. To our knowledge, this is the first work tackling Goss’s problem when the base ring has class number strictly greater than 1. |
| first_indexed | 2024-03-11T19:50:51Z |
| format | Article |
| id | doaj.art-e07c52bb26e04d8ab843c14b03642d7e |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-03-11T19:50:51Z |
| publishDate | 2023-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-e07c52bb26e04d8ab843c14b03642d7e2023-10-05T09:42:34ZengCambridge University PressForum of Mathematics, Sigma2050-50942023-01-011110.1017/fms.2023.94Algebraic relations among Goss’s zeta values on elliptic curvesNathan Green0Tuan Ngo Dac1Louisiana Tech University, 501 Dan Reneau Dr, 71270, USA; E-mail:Normandie Université, Université de Caen Normandie - CNRS, Laboratoire de Mathématiques Nicolas Oresme (LMNO), UMR 6139, Caen, 14000, France; E-mail:In 2007 Chang and Yu determined all the algebraic relations among Goss’s zeta values for $A=\mathbb F_q[\theta ]$ , also known as the Carlitz zeta values. Goss raised the problem of determining all algebraic relations among Goss’s zeta values at positive integers for a general base ring A, but very little is known. In this paper, we develop a general method, and we determine all algebraic relations among Goss’s zeta values for the base ring A which is the coordinate ring of an elliptic curve defined over $\mathbb F_q$ . To our knowledge, this is the first work tackling Goss’s problem when the base ring has class number strictly greater than 1.https://www.cambridge.org/core/product/identifier/S2050509423000944/type/journal_article11J9311G0911M38 |
| spellingShingle | Nathan Green Tuan Ngo Dac Algebraic relations among Goss’s zeta values on elliptic curves Forum of Mathematics, Sigma 11J93 11G09 11M38 |
| title | Algebraic relations among Goss’s zeta values on elliptic curves |
| title_full | Algebraic relations among Goss’s zeta values on elliptic curves |
| title_fullStr | Algebraic relations among Goss’s zeta values on elliptic curves |
| title_full_unstemmed | Algebraic relations among Goss’s zeta values on elliptic curves |
| title_short | Algebraic relations among Goss’s zeta values on elliptic curves |
| title_sort | algebraic relations among goss s zeta values on elliptic curves |
| topic | 11J93 11G09 11M38 |
| url | https://www.cambridge.org/core/product/identifier/S2050509423000944/type/journal_article |
| work_keys_str_mv | AT nathangreen algebraicrelationsamonggossszetavaluesonellipticcurves AT tuanngodac algebraicrelationsamonggossszetavaluesonellipticcurves |