q-Identities for Maass waveforms.
Given a finite -group acting on a smooth projective curve over an algebraically closed field of characteristic , the dimension of the tangent space of the associated equivariant deformation functor is equal to the dimension of the space of coinvariants of acting on the space of global holomorphic quadratic differentials on . We apply known results about the Galois module structure of Riemann-Roch spaces to compute this dimension when is cyclic or when the action of on is weakly...
In any normal number field having Q₈, the quaternion group of order 8, as Galois group over the rationals, at least two finite primes must ramify. The classical example by Dedekind of such a field is extraordinary in that it is totally real and only the primes 2 and 3 are ramified. In this note we describe in detail all Q₈-fields over the rationals where only two (finite) primes are ramified. We also show that, for any integer n>3 and any prime , there exist unique real and complex normal number...