On the sign changes of the coefficients attached to triple product L-functions

Abstract

Let [Formula: see text] and [Formula: see text] be two distinct normalized primitive holomorphic cusp forms of even integral weights [Formula: see text] and [Formula: see text] for the full modular group SL[Formula: see text], respectively. In this paper, we investigate the sign changes of the sequence [Formula: see text] in short intervals, where [Formula: see text] denote the normalized coefficients of triple product [Formula: see text]-functions [Formula: see text] attached to [Formula: see text] and [Formula: see text], respectively. We provide quantitative results for the number of sign changes of the sequences mentioned above in short intervals.