Remarks on a special value of the Selberg zeta function
| dc.creator | Templier, Nicolas | |
| dc.date | 2009-02-24 | |
| dc.date | 2009-02-25 | |
| dc.date.accessioned | 2026-07-07T12:46:18Z | |
| dc.date.available | 2026-07-07T12:46:18Z | |
| dc.description | Let $\CmZ_{Y_0(N)}$ be the constant term of the logarithmic derivative at $s=1$ of the Selberg zeta function of the modular curve $Y_0(N)$. Jorgenson and Kramer established the bound $\CmZ_{Y_0(N)}=O_ε(N^ε)$, $ε>0$ by relating it to geometric invariants. In this article we give, for $N$ prime, another proof via $L$-functions and exponential sums improving on a previous approach by Abbes-Ullmo and Michel-Ullmo. We further derive a power of $\log N$ bound along the same line. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/0902.4225 | |
| dc.identifier | http://arxiv.org/abs/0902.4225 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221335 | |
| dc.subject | Number Theory | |
| dc.subject | Spectral Theory | |
| dc.subject | 11M36; 11L05 | |
| dc.title | Remarks on a special value of the Selberg zeta function | |
| dc.type | text |