We study the simultaneous sign change of Fourier coefficients of a pair of distinct normalized newforms of integral weight supported on primes power indices, we also prove some equidistribution results. Finally, we consider an analogous question for Fourier coefficients of a pair of half-integral weight Hecke eigenforms. (2010): 11F03, 11F30, 11F37
Mathematics subject classification
In this paper, we discuss questions related to the oscillatory behavior and the equidistribution of signs for certain subfamilies of Fourier coefficients of integral weight newforms with a nontrivial nebentypus as well as Fourier coefficients of eigenforms of half-integral weight reachable by the Shimura correspondence.
In this paper, we investigate the "angular changes" behavior of some subfamilies of Fourier coefficients of both integral and half-integral weight holomorphic cusp forms, thus one gets information about signs of the real an imaginary parts of these subfamilies. These give an extension of some recent results of Kohnen and his collaborators.
Let f be a cusp form of half-integral weight k + 1/2, whose Fourier coefficients a(n) not necessarily real. We prove an extension of the Bruinier-Kohnen conjecture on the equidistribution of the signs of a(n) for the families {a(tp 2ν )} p,prime , where ν and t be fixed odd positive integer and square-free integer respectively.
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