Counting elements of the congruence subgroup
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866913604916215808 |
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| author | Bulinski, Kamil Shparlinski, Igor E. |
| author_facet | Bulinski, Kamil Shparlinski, Igor E. |
| contents | We obtain asymptotic formulas for the number of matrices in the congruence subgroup \[ Γ_0(Q) = \left\{ A\in\mathrm{SL}_2(\mathbb Z):~c \equiv 0 \pmod Q\right\}, \] which are of naive height at most $X$. Our result is uniform in a very broad range of values $Q$ and $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_10485 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Counting elements of the congruence subgroup Bulinski, Kamil Shparlinski, Igor E. Number Theory We obtain asymptotic formulas for the number of matrices in the congruence subgroup \[ Γ_0(Q) = \left\{ A\in\mathrm{SL}_2(\mathbb Z):~c \equiv 0 \pmod Q\right\}, \] which are of naive height at most $X$. Our result is uniform in a very broad range of values $Q$ and $X$. |
| title | Counting elements of the congruence subgroup |
| topic | Number Theory |
| url | https://arxiv.org/abs/2308.10485 |