A note on Maass forms of icosahedral type

Using ideas of Ramakrishnan, we consider the icosahedral analogue of the theorems of Sarnak and Brumley on Hecke-Maass newforms with Fourier coefficients in a quadratic order. Although we are unable to conclude the existence of an associated Galois representation in this case, we show that one can deduce some implications of such an association, including weak automorphy of all symmetric powers and the value distribution of Fourier coefficients predicted by the Chebotarev density theorem.Comment: 9 pages, to appear in Mathematische Zeitschrif

Ideals associated to two sequences and a matrix

Let \u_{1\times n}, \X_{n\times n}, and \v_{n\times 1} be matrices of indeterminates, \Adj \X be the classical adjoint of \X, and $H(n)$ be the ideal I_1(\u\X)+I_1(\X\v)+I_1(\v\u-\Adj \X). Vasconcelos has conjectured that $H(n)$ is a perfect Gorenstein ideal of grade $2n$. In this paper, we obtain the minimal free resolution of $H(n)$; and thereby establish Vasconcelos' conjecture