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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2308.14681 |
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| _version_ | 1866913901764935680 |
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| author | Lee, Sung Min |
| author_facet | Lee, Sung Min |
| contents | In 2009, W. D. Banks and I. E. Shparlinski studied the average densities of primes $p \leq x$ for which the reductions of elliptic curves of small height modulo $p$ satisfy certain arithmetic properties, namely cyclicity and divisibility of the number of points by a fixed integer $m$. In this paper, we refine their results, restricting the primes $p$ under consideration to lie in an arithmetic progression $k \bmod{n}$. Furthermore, for a fixed modulus $n$, we investigate statistical biases among the different congruence classes $k \bmod{n}$ of primes satisfying the aforementioned properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_14681 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the average congruence class bias for cyclicity and divisibility of the groups of $\mathbb{F}_p$-points of elliptic curves Lee, Sung Min Number Theory In 2009, W. D. Banks and I. E. Shparlinski studied the average densities of primes $p \leq x$ for which the reductions of elliptic curves of small height modulo $p$ satisfy certain arithmetic properties, namely cyclicity and divisibility of the number of points by a fixed integer $m$. In this paper, we refine their results, restricting the primes $p$ under consideration to lie in an arithmetic progression $k \bmod{n}$. Furthermore, for a fixed modulus $n$, we investigate statistical biases among the different congruence classes $k \bmod{n}$ of primes satisfying the aforementioned properties. |
| title | On the average congruence class bias for cyclicity and divisibility of the groups of $\mathbb{F}_p$-points of elliptic curves |
| topic | Number Theory |
| url | https://arxiv.org/abs/2308.14681 |