The Investigation of the Discrete Universality of L-Functions of Elliptic Curves
In the paper, we prove the discrete universality theorem in the sense of the weak convergence of probability measures in the space of analytic functions for the L-functions of elliptic curves. We consider an approximation of analytic functions by translations LE (s+imh) , where h > 0 is a fixed...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2022-12-01
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| Series: | Jaunųjų Mokslininkų Darbai |
| Subjects: | |
| Online Access: | https://zurnalai.vu.lt/jaunuju-mokslininku-darbai/article/view/27428 |
| _version_ | 1797829760642973696 |
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| author | Samanta Zakaitė Antanas Garbaliauskas |
| author_facet | Samanta Zakaitė Antanas Garbaliauskas |
| author_sort | Samanta Zakaitė |
| collection | DOAJ |
| description |
In the paper, we prove the discrete universality theorem in the sense of the weak convergence of probability measures in the space of analytic functions for the L-functions of elliptic curves. We consider an approximation of analytic functions by translations LE (s+imh) , where h > 0 is a fixed number, the translations of the imaginary part of the complex variable take values from some discrete set such as arithmetical progression. We suppose that the number h > 0 is chosen so that exp{2πk/h } is an rational number for some non-zero integer. The proof of discrete universality of the derivatives of L-functions of elliptic curves is based on a limit theorem in the sense of weak convergence of probability measures in the space of analytic functions.
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| first_indexed | 2024-04-09T13:26:25Z |
| format | Article |
| id | doaj.art-73a3d774a2734e4882750e0fe2b5f51b |
| institution | Directory Open Access Journal |
| issn | 1648-8776 |
| language | English |
| last_indexed | 2024-04-09T13:26:25Z |
| publishDate | 2022-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Jaunųjų Mokslininkų Darbai |
| spelling | doaj.art-73a3d774a2734e4882750e0fe2b5f51b2023-05-10T09:46:54ZengVilnius University PressJaunųjų Mokslininkų Darbai1648-87762022-12-0152110.15388/JMD.2022.12The Investigation of the Discrete Universality of L-Functions of Elliptic CurvesSamanta ZakaitėAntanas Garbaliauskas0Šiauliai State Higher Education Institution, Lithuania In the paper, we prove the discrete universality theorem in the sense of the weak convergence of probability measures in the space of analytic functions for the L-functions of elliptic curves. We consider an approximation of analytic functions by translations LE (s+imh) , where h > 0 is a fixed number, the translations of the imaginary part of the complex variable take values from some discrete set such as arithmetical progression. We suppose that the number h > 0 is chosen so that exp{2πk/h } is an rational number for some non-zero integer. The proof of discrete universality of the derivatives of L-functions of elliptic curves is based on a limit theorem in the sense of weak convergence of probability measures in the space of analytic functions. https://zurnalai.vu.lt/jaunuju-mokslininku-darbai/article/view/27428L-function of elliptic curveslimit theoremdiscrete universality |
| spellingShingle | Samanta Zakaitė Antanas Garbaliauskas The Investigation of the Discrete Universality of L-Functions of Elliptic Curves Jaunųjų Mokslininkų Darbai L-function of elliptic curves limit theorem discrete universality |
| title | The Investigation of the Discrete Universality of L-Functions of Elliptic Curves |
| title_full | The Investigation of the Discrete Universality of L-Functions of Elliptic Curves |
| title_fullStr | The Investigation of the Discrete Universality of L-Functions of Elliptic Curves |
| title_full_unstemmed | The Investigation of the Discrete Universality of L-Functions of Elliptic Curves |
| title_short | The Investigation of the Discrete Universality of L-Functions of Elliptic Curves |
| title_sort | investigation of the discrete universality of l functions of elliptic curves |
| topic | L-function of elliptic curves limit theorem discrete universality |
| url | https://zurnalai.vu.lt/jaunuju-mokslininku-darbai/article/view/27428 |
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