Triple Product L values and Dihedral Congruences for Cusp Forms
Let be a prime, and In this paper, we prove that a certain trace of normalized, rightmost critical values of triple product L functions, of cuspidal Hecke eigenforms of level one and weight k, is non integral at p if and only if the class number We use the Bloch Kato conjecture to explain this, using "dihedral" congruences, modulo a divisor of p, for cuspidal Hecke eigenforms of level one and weight k (e.g. p 23, k 12, g D) Exploiting the Galois interpretation of such congruences, we may produce global torsion elements which contribute to the denominator of the conjectural formula for some L value contributing to the trace.