On a divisor problem related to the Epstein zeta-function, IV
We characterize all the cases in which products of arbitrary numbers of nearly holomorphic eigenforms and products of arbitrary numbers of quasimodular eigenforms for the full modular group SL₂(ℤ) are again eigenforms.
We consider to be the -function attached to a particular automorphic form on . We establish an upper bound for the mean square estimate on the critical line of Rankin-Selberg -function . As an application of this result, we give an asymptotic formula for the discrete sum of coefficients of .
We study the average of the Fourier coefficients of a holomorphic cusp form for the full modular group at primes of the form [g(n)].
Let , and be three distinct primitive holomorphic cusp forms of even integral weights , and for the full modular group , respectively, and let , and denote the th normalized Fourier coefficients of , and , respectively. We consider the cancellations of sums related to arithmetic functions , twisted by and establish the following results: for any , where , are any fixed positive integers.