The Sato -Tate conjecture for a picard curve with complex multiplication
Let C/Q be the genus 3 Picard curve given by the affine model y^3=x^4-x. In this Master thesis we compute its Sato-Tate group, show the generalized Sato-Tate conjecture for C, and compute the statistical moments for the limiting distribution of the normalized local factors of C.
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| Format: | master thesis |
| Publication Date: | 2014 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2099.1/22928 |
| Online Access: | https://hdl.handle.net/2099.1/22928 |
| Access Level: | Open access |
| Keyword: | Number theory Sato-Tate conjecture Number Theory Picard curve Distribution Nombres, Teoria dels Classificació AMS::11 Number theory::11Y Computational number theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres |
| Summary: | Let C/Q be the genus 3 Picard curve given by the affine model y^3=x^4-x. In this Master thesis we compute its Sato-Tate group, show the generalized Sato-Tate conjecture for C, and compute the statistical moments for the limiting distribution of the normalized local factors of C. |
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