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- W4309804080 abstract "Fix a prime number $p$. Let $mathbb{F}_q$ be a finite field of characteristic coprime to 2, 3, and $p$, which also contains the primitive $p$-th root of unity $mu_p$. Based on the works by Swinnerton-Dyer and Klagsbrun, Mazur, and Rubin, we prove that the probability distribution of the sizes of prime Selmer groups over a family of cyclic prime twists of non-isotrivial elliptic curves over $mathbb{F}_q(t)$ satisfying a number of mild constraints conforms to the distribution conjectured by Bhargava, Kane, Lenstra, Poonen, and Rains with explicit error bounds. The key tools used in proving these results are the Riemann hypothesis over global function fields, the Erdos-Kac theorem, and the geometric ergodicity of Markov chains." @default.
- W4309804080 created "2022-11-29" @default.
- W4309804080 creator A5071934989 @default.
- W4309804080 date "2022-11-21" @default.
- W4309804080 modified "2023-10-14" @default.
- W4309804080 title "On the prime Selmer ranks of cyclic prime twist families of elliptic curves over global function fields" @default.
- W4309804080 doi "https://doi.org/10.48550/arxiv.2211.11486" @default.
- W4309804080 hasPublicationYear "2022" @default.
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