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- W3205377746 abstract "Abstract We explicitly construct the Dirichlet series $$begin{equation*}L_{mathrm{Tam}}(s):=sum_{m=1}^{infty}frac{P_{mathrm{Tam}}(m)}{m^s},end{equation*}$$ where $P_{mathrm{Tam}}(m)$ is the proportion of elliptic curves $E/mathbb{Q}$ in short Weierstrass form with Tamagawa product m. Although there are no $E/mathbb{Q}$ with everywhere good reduction, we prove that the proportion with trivial Tamagawa product is $P_{mathrm{Tam}}(1)={0.5053dots}$. As a corollary, we find that $L_{mathrm{Tam}}(-1)={1.8193dots}$ is the average Tamagawa product for elliptic curves over $mathbb{Q}$. We give an application of these results to canonical and Weil heights." @default.
- W3205377746 created "2021-10-25" @default.
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- W3205377746 date "2020-12-01" @default.
- W3205377746 modified "2023-09-24" @default.
- W3205377746 title "Tamagawa Products of Elliptic Curves Over ℚ" @default.
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- W3205377746 doi "https://doi.org/10.1093/qmath/haab042" @default.
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