Simultaneous sign change of Fourier-coefficients of two cusp forms

On signs of Hecke eigenvalues of Siegel eigenforms

“…The aim of this section is to show that the degree of the polynomial, appearing in the Euler product of a certain Dirichlet series with coefficients the product of eigenvalues at prime powers for a fixed prime, is at most 14. This result improves on a result of Gun et al [8,Lemma 15]. Though the result of Gun et al is sufficient for our purpose, we would like to present the proof of our result since it gives a better result by following a completely different but elementary approach compared to [8, Lemma 15].…”

Simultaneous behaviour of the Fourier coefficients of two Hilbert modular cusp forms

“…In [2], the authors, by using an elementary observation about real zeros of Dirichlet series instead of bounded denominators argument, strengthen the results of [4], by doing away with the Galois conjugacy condition and in fact, they extended the result to cusp forms with arbitrary real Fourier coefficients.…”

“…Case (2): Suppose that at least one of α p , β p is 0 or π, say α p = 0 or π and β p ∈ (0, π). If β p /π / ∈ Q, there is nothing to prove.…”

The first simultaneous sign change and non-vanishing of Hecke eigenvalues of newforms

“…Here we study first sign change and non-vanishing of the sequence {a f (n)a g (n)} n∈N . The question of simultaneous sign change for arbitrary cusp forms was first studied by Kohnen and Sengupta [14] under certain conditions which were later removed by the first author, Kohnen and Rath [9]. In the later paper, the authors prove infinitely many sign change of the sequence {a f (n)a g (n)} n∈N .…”