We focus on the problems of sign changes and nonvanishing of Fourier coefficients of holomorphic cusp forms. Let , and be the -th Fourier coefficients of primitive holomorphic cusp forms , and for , respectively. Firstly, we study the behavior of the signs of the sequences with , with , and in short intervals, and present some quantitative results for the number of sign changes for . Here we improve and generalize previous results. Moreover, we investigate simultaneous nonvanishing of with in short intervals.
"Sign changes and nonvanishing of Fourier coefficients of holomorphic cusp forms." Rocky Mountain J. Math. 51 (5) 1701 - 1714, October 2021. https://doi.org/10.1216/rmj.2021.51.1701