Symmetric square L-values and dihedral congruences for cusp forms |
| |
Authors: | Neil Dummigan Bernhard Heim |
| |
Affiliation: | a University of Sheffield, Department of Pure Mathematics, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, UK b German University of Technology in Oman (GUtech), Department of Applied Information Technology, PO Box 1816 Athaibah, PC 130, Corner of Beach Road and Wadi Athaibah Way, Sultanate of Oman |
| |
Abstract: | Let be a prime, and k=(p+1)/2. In this paper we prove that two things happen if and only if the class number . One is the non-integrality at p of a certain trace of normalised critical values of symmetric square L-functions, of cuspidal Hecke eigenforms of level one and weight k. The other is the existence of such a form g whose Hecke eigenvalues satisfy “dihedral” congruences modulo a divisor of p (e.g. p=23, k=12, g=Δ). We use the Bloch-Kato conjecture to link these two phenomena, using the Galois interpretation of the congruences to produce global torsion elements which contribute to the denominator of the conjectural formula for an L-value. When , the trace turns out always to be a p-adic unit. |
| |
Keywords: | 11F67 11B68 11E41 11F33 11F80 |
本文献已被 ScienceDirect 等数据库收录! |
|