Numerical Evidence Toward a 2-adic Equivariant "Main Conjecture"

1. The conjecture Let K be a totally real finite Galois extension of Q with Galois group G dihedral of order 8, and suppose that √ 2 is not in K. Fix a finite set S of primes of Q including 2, ∞ and all primes that ramify in K. Let C be the cyclic subgroup of G of order 4 and F the fixed field of C acting on K. Fix a 2-adic unit u ≡ 5 mod 8Z 2. Write L F (s, χ) for the 2-adic L-functions, normalized as in [W], of the 2-adic characters χ of C or, equivalently by class field theory, of the corresponding 2-adic primitive ray class characters. We always work with their S-truncated forms