On the number of binary quadratic forms having discriminant $1-4p$, $p$ prime
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866912895206424576 |
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| author | Miller, Alison Beth Xiao, Stanley Yao |
| author_facet | Miller, Alison Beth Xiao, Stanley Yao |
| contents | In this paper we obtain an asymptotic formula for the number of $\operatorname{SL}_2(\mathbb{Z})$-equivalence classes of positive definite binary quadratic forms over $\bZ$ having bounded discriminant $Δ= 1-4p$, with $p$ a prime. We also give a random Euler product model for the distribution of Hurwitz class numbers, which is supported by our formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_06559 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the number of binary quadratic forms having discriminant $1-4p$, $p$ prime Miller, Alison Beth Xiao, Stanley Yao Number Theory In this paper we obtain an asymptotic formula for the number of $\operatorname{SL}_2(\mathbb{Z})$-equivalence classes of positive definite binary quadratic forms over $\bZ$ having bounded discriminant $Δ= 1-4p$, with $p$ a prime. We also give a random Euler product model for the distribution of Hurwitz class numbers, which is supported by our formula. |
| title | On the number of binary quadratic forms having discriminant $1-4p$, $p$ prime |
| topic | Number Theory |
| url | https://arxiv.org/abs/2011.06559 |