A formula for the central value of certain Hecke L-functions
| dc.creator | Pacetti, Ariel | |
| dc.date | 2003-09-01 | |
| dc.date | 2004-12-22 | |
| dc.date.accessioned | 2026-07-07T05:00:44Z | |
| dc.date.available | 2026-07-07T05:00:44Z | |
| dc.description | Let N = 1 mod 4 be the negative of a prime, K=Q(sqrt{N}) and O_K its ring of integers. Let D be a prime ideal in O_K of prime norm congruent to 3 modulo 4. Under these assumptions, there exists Hecke characters $ψ_{\D}$ of K with conductor $(\D)$ and infinite type $(1,0)$. Their L-series L(ψ_\D,s)$ are associated to a CM elliptic curve E(N,\D) defined over the Hilbert class field of $K$. We will prove a Waldspurger-type formula for L(ψ_\D,s) of the form L(ψ_\D,1) = Ω\sum_{[\A],I} r(\D,[\A],I) m_{[\A],I}([\D]) where the sum is over class ideal representatives I of a maximal order in the quaternion algebra ramified at |N| and infinity and [\A] are class group representatives of $K$. An application of this formula for the case N=-7 will allow us to prove the non-vanishing of a family of L-series of level $7|D|$ over $K$. | |
| dc.description | 43 pages | |
| dc.identifier | https://arxiv.org/abs/math/0309023 | |
| dc.identifier | http://arxiv.org/abs/math/0309023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68433 | |
| dc.subject | Number Theory | |
| dc.subject | 11G40 | |
| dc.title | A formula for the central value of certain Hecke L-functions | |
| dc.type | text |