Uniform effective estimates for $\vert L(1,χ)\vert$
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866912746884300800 |
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| author | Languasco, Alessandro Trudgian, Timothy S. |
| author_facet | Languasco, Alessandro Trudgian, Timothy S. |
| contents | Let $L(s,χ)$ be the Dirichlet $L$-function associated to a non-principal primitive Dirichlet character $χ$ defined modulo $q$, where $q\ge 3$. We prove, under the assumption of the Generalised Riemann Hypothesis, the validity of estimates given by Lamzouri, Li, and Soundararajan on $\vert L(1,χ) \vert$. As a corollary, we have that similar estimates hold for the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{-q})$, $q\ge 5$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2011_08348 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Uniform effective estimates for $\vert L(1,χ)\vert$ Languasco, Alessandro Trudgian, Timothy S. Number Theory 11M20, 33-04, 11Y16, 11Y99, 33B15 Let $L(s,χ)$ be the Dirichlet $L$-function associated to a non-principal primitive Dirichlet character $χ$ defined modulo $q$, where $q\ge 3$. We prove, under the assumption of the Generalised Riemann Hypothesis, the validity of estimates given by Lamzouri, Li, and Soundararajan on $\vert L(1,χ) \vert$. As a corollary, we have that similar estimates hold for the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{-q})$, $q\ge 5$. |
| title | Uniform effective estimates for $\vert L(1,χ)\vert$ |
| topic | Number Theory 11M20, 33-04, 11Y16, 11Y99, 33B15 |
| url | https://arxiv.org/abs/2011.08348 |