Academic Journal
On the zeta functions of supersingular isogeny graphs and modular curves
| Title: | On the zeta functions of supersingular isogeny graphs and modular curves |
|---|---|
| Authors: | Antonio Lei, Katharina Müller |
| Source: | Archiv der Mathematik. 122:285-294 |
| Publication Status: | Preprint |
| Publisher Information: | Springer Science and Business Media LLC, 2023. |
| Publication Year: | 2023 |
| Subject Terms: | Mathematics - Number Theory, Ihara zeta functions, modular curves, Enumeration in graph theory, supersingular isogeny graphs, Modular and Shimura varieties, 11M41, 05C30, 11G18, 14G35, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO), Other Dirichlet series and zeta functions, Arithmetic aspects of modular and Shimura varieties, Hasse-Weil zeta functions |
| Description: | Let $p$ and $q$ be distinct prime numbers, with $q\equiv 1\pmod{12}$. Let $N$ be a positive integer that is coprime to $pq$. We prove a formula relating the Hasse--Weil zeta function of the modular curve $X_0(qN)_{\mathbb{F}_q}$ to the Ihara zeta function of the $p$-isogeny graphs of supersingular elliptic curves defined over $\overline{\mathbb{F}_q}$ equipped with a $Γ_0(N)$-level structure. When $N=1$, this recovers a result of Sugiyama. minor changes, accepted for publication in Archiv der Mathematik |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1420-8938 0003-889X |
| DOI: | 10.1007/s00013-023-01937-z |
| DOI: | 10.48550/arxiv.2307.01001 |
| Access URL: | http://arxiv.org/abs/2307.01001 https://zbmath.org/7806706 https://doi.org/10.1007/s00013-023-01937-z |
| Rights: | Springer Nature TDM CC BY |
| Accession Number: | edsair.doi.dedup.....fc2125321ebaf1e5412bf3a0cf30e5a9 |
| Database: | OpenAIRE |
| ISSN: | 14208938 0003889X |
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| DOI: | 10.1007/s00013-023-01937-z |