Natural boundaries for Euler products of Igusa zeta functions of elliptic curves
We study the analytic behavior of adelic versions of Igusa integrals given by integer polynomials defining elliptic curves. By applying results on the meromorphic continuation of symmetric power L-functions and the Sato–Tate conjectures, we prove that these global Igusa zeta functions have some mero...
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| Format: | Journal article |
| Language: | English |
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World Scientific Publishing
2018
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| _version_ | 1826283074795601920 |
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| author | du Sautoy, M |
| author_facet | du Sautoy, M |
| author_sort | du Sautoy, M |
| collection | OXFORD |
| description | We study the analytic behavior of adelic versions of Igusa integrals given by integer polynomials defining elliptic curves. By applying results on the meromorphic continuation of symmetric power L-functions and the Sato–Tate conjectures, we prove that these global Igusa zeta functions have some meromorphic continuation until a natural boundary beyond which no continuation is possible. |
| first_indexed | 2024-03-07T00:53:27Z |
| format | Journal article |
| id | oxford-uuid:87314b4b-e680-48f0-b6e1-84da6b4731bd |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:53:27Z |
| publishDate | 2018 |
| publisher | World Scientific Publishing |
| record_format | dspace |
| spelling | oxford-uuid:87314b4b-e680-48f0-b6e1-84da6b4731bd2022-03-26T22:09:06ZNatural boundaries for Euler products of Igusa zeta functions of elliptic curvesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:87314b4b-e680-48f0-b6e1-84da6b4731bdEnglishSymplectic Elements at OxfordWorld Scientific Publishing2018du Sautoy, MWe study the analytic behavior of adelic versions of Igusa integrals given by integer polynomials defining elliptic curves. By applying results on the meromorphic continuation of symmetric power L-functions and the Sato–Tate conjectures, we prove that these global Igusa zeta functions have some meromorphic continuation until a natural boundary beyond which no continuation is possible. |
| spellingShingle | du Sautoy, M Natural boundaries for Euler products of Igusa zeta functions of elliptic curves |
| title | Natural boundaries for Euler products of Igusa zeta functions of elliptic curves |
| title_full | Natural boundaries for Euler products of Igusa zeta functions of elliptic curves |
| title_fullStr | Natural boundaries for Euler products of Igusa zeta functions of elliptic curves |
| title_full_unstemmed | Natural boundaries for Euler products of Igusa zeta functions of elliptic curves |
| title_short | Natural boundaries for Euler products of Igusa zeta functions of elliptic curves |
| title_sort | natural boundaries for euler products of igusa zeta functions of elliptic curves |
| work_keys_str_mv | AT dusautoym naturalboundariesforeulerproductsofigusazetafunctionsofellipticcurves |