The 2-adic valuations of the algebraic central $L$-values for quadratic twists of weight 2 newforms
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915539860848640 |
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| author | Adachi, Taiga Nomoto, Keiichiro Shii, Ryota |
| author_facet | Adachi, Taiga Nomoto, Keiichiro Shii, Ryota |
| contents | Let $f$ be a normalized newform of weight 2 on $Γ_0(N)$ whose coefficients lie in $\mathbb{Q}$ and let $χ_M$ be a primitive quadratic Dirichlet character with conductor $M$. In this paper, under mild assumptions on $M$, we give a sharp lower bound of the 2-adic valuation of the algebraic central $L$-value $L(f, χ_M, 1)$ and evaluate the 2-adic valuation for an infinite number of $M$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_11474 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The 2-adic valuations of the algebraic central $L$-values for quadratic twists of weight 2 newforms Adachi, Taiga Nomoto, Keiichiro Shii, Ryota Number Theory Let $f$ be a normalized newform of weight 2 on $Γ_0(N)$ whose coefficients lie in $\mathbb{Q}$ and let $χ_M$ be a primitive quadratic Dirichlet character with conductor $M$. In this paper, under mild assumptions on $M$, we give a sharp lower bound of the 2-adic valuation of the algebraic central $L$-value $L(f, χ_M, 1)$ and evaluate the 2-adic valuation for an infinite number of $M$. |
| title | The 2-adic valuations of the algebraic central $L$-values for quadratic twists of weight 2 newforms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2403.11474 |