Siegel's Modular Forms and the Arithmetic of Quadratic Forms.
We examine an arithmetical function defined by recursion relations on the sequence and obtain sufficient condition(s) for the sequence to change sign infinitely often. As an application we give criteria for infinitely many sign changes of Chebyshev polynomials and that of sequence formed by the Fourier coefficients of a cusp form.
We prove that the complete -functions of classical holomorphic newforms have infinitely many simple zeros.
Our aim in this paper is to prove congruences between on the one hand certain eigenforms of level and weight greater than 2 and on the other hand twists of eigenforms of level and weight 2. One knows a priori that such congruences exist; the novelty here is that we determine the character of the form of weight 2 and the twist in terms of the slope of the higher weight form, i.e., in terms of the valuation of its eigenvalue for . Curiously, we also find a relation between the leading terms of...