Simultaneous non-vanishing and sign changes of Fourier coefficients of modular forms.

In this paper, we give some results on simultaneous non-vanishing and simultaneous sign-changes for the Fourier coefficients of two modular forms. More precisely, given two modular forms f and g with Fourier coefficients a n and b n respectively, we consider the following questions: existence of infinitely many primes p such that a p b p ≠ 0 ; simultaneous non-vanishing in the short intervals and in arithmetic progressions; simultaneous sign changes in short intervals. [ABSTRACT FROM AUTHOR]