On Analytic Functions which have Algebraic Values at a Convergent Sequence of Points

On the values of a class of analytic functions at algebraic points

We introduce a class of analytic functions of number theoretic interest, namely stammering functions. It has been recently proved that these functions take transcendental values at some algebraic points. In the present paper, we establish a general transcendence criterion that extends these results. Another aim is to underline the main difficulties arising from the use of the Schmidt Subspace T...

Algebraic Values of Transcendental Functions at Algebraic Points

In this paper, the authors will prove that any subset of Q can be the exceptional set of some transcendental entire function. Furthermore, we could generate this theorem to a much more general version and present a unified proof.

Algebraic values of analytic functions

Given an analytic function of one complex variable f , we investigate the arithmetic nature of the values of f at algebraic points. A typical question is whether f(α) is a transcendental number for each algebraic number α. Since there exist transcendental entire functions f such that f (t)(α) ∈ Q[α] for any t ≥ 0 and any algebraic number α, one needs to restrict the situation by adding hypothes...

Fixed Points of Analytic Functions

Special values of Green functions at big CM points

We give a formula for the values of automorphic Green functions on the special rational 0-cycles (big CM points) attached to certain maximal tori in the Shimura varieties associated to rational quadratic spaces of signature (2d, 2). Our approach depends on the fact that the Green functions in question are constructed as regularized theta lifts of harmonic weak Maass forms, and it involves the S...