Oscillations of Fourier coefficients of modular forms

On dirichlet series related to certain cusp forms

“…Clearly, from (3) we have that Icpl < 2. On the other hand, M. Ram Murty [16] proved that, for an arbitrary e > 0, for a positive density of primes. R. A. Rankin [17] …”

On Hecke eigenvalues at Piatetski-Shapiro primes

“…Under the generalized Riemann hypothesis for modular L-functions, the right-hand side of (1.2) can be replaced by N 1/2+ε . M. R. Murty [22] conjectured an Ω-result of the form p≤N λ f (p) = Ω ± √ N log log log N log N and succeeded in proving it provided some L-function has no real zero between 1/2 and 1. S. D. Adhikari [1] generalized this result to cusp forms for the group Γ 0 (N ).…”

On the Number of Sign Changes of Hecke Eigenvalues of Newforms

“…On the other hand, if N = 1 and k ≡ 0 (mod 4) or if N > 1, the method of Siegel [12] does not apply and thus a different approach, based on analytic number theory estimates, has been developed by Kohnen and Sengupta [9], which in turn is related to some ideas of Murty [10].…”