The Steinberg Symbol and Special Values of L-functions
| dc.creator | Busuioc, Cecilia | |
| dc.date | 2006-09-21 | |
| dc.date | 2006-10-27 | |
| dc.date.accessioned | 2026-07-07T07:25:03Z | |
| dc.date.available | 2026-07-07T07:25:03Z | |
| dc.description | The main results of this article concern the definition of a compactly supported cohomology class for the congruence group $Γ_0(p^n)$ with values in the second Milnor $K$-group (modulo 2-torsion) of the ring of $p$-integers of the cyclotomic extension $\Q(μ_{p^n})$. We endow this cohomology group with a natural action of the standard Hecke operators and discuss the existence of special Hecke eigenclasses in its parabolic cohomology. Moreover, for $n=1$, assuming the non-degeneracy of a certain pairing on $p$-units induced by the Steinberg symbol when $(p,k)$ is an irregular pair, i.e. $p|\frac{B_k}{k}$, we show that the values of the above pairing are congruent mod $p$ to the $L$-values of a weight $k$, level 1 cusp form which satisfies Eisenstein-type congruences mod $p$, a result that was predicted by a conjecture of R. Sharifi. | |
| dc.description | corrected typos, slight enhancement of Theorem 1.2 with details added in section 7 | |
| dc.identifier | https://arxiv.org/abs/math/0609588 | |
| dc.identifier | http://arxiv.org/abs/math/0609588 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116597 | |
| dc.subject | Number Theory | |
| dc.subject | 11F67(Primary) 19F15(Secondary) | |
| dc.title | The Steinberg Symbol and Special Values of L-functions | |
| dc.type | text |