A spectral interpretation of the zeros of the constant term of certain Eisenstein series
| dc.creator | Mueller, Werner | |
| dc.date | 2007-03-12 | |
| dc.date.accessioned | 2026-07-07T07:51:27Z | |
| dc.date.available | 2026-07-07T07:51:27Z | |
| dc.description | In this paper we consider the constant term $ϕ_K(y,s)$ of the non-normalized Eisenstein series attached to $\PSL(2,\cO_K)$, where $K$ is either $\Q$ or an imaginary quadratic field of class number one. The main purpose of this paper is to show that for every $a\ge 1$ the zeros of the Dirichlet series $ϕ_K(a,s)$ admit a spectral interpretation in terms of eigenvalues of a natural self-adjoint operator $Δ_a$. This implies that, except for at most two real zeros, all zeros of $ϕ_K(a,s)$ are on the critical line, and all zeros are simple. For $K=\Q$ this is due to Lagarias and Suzuki and Ki. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703340 | |
| dc.identifier | http://arxiv.org/abs/math/0703340 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125516 | |
| dc.subject | Number Theory | |
| dc.subject | Spectral Theory | |
| dc.subject | 11M36, 11M26 | |
| dc.title | A spectral interpretation of the zeros of the constant term of certain Eisenstein series | |
| dc.type | text |