ON THE ZEROS OF THE RAMANUJAN TAU-DIRICHLET SERIES IN THE CRITICAL STRIP

We describe computations which show that each of the first 12069 zeros of the Ramanujan tau-Dirichlet series of the form sigma + it in the r egion 0 < t < 6397 is simple and lies on the line sigma = 6. The failu res of Gram's law in this region are also noted. The first 5018 zeros and 2228 successive zeros beginning with the 20001st zero are also cal culated. The distribution of the normalized spacing of the zeros is ex amined and it appears to be that of the eigenvalues of random matrices . These comptuations are done with a Berry-Keating formula for the T-D irichlet series and evaluated using Mathematica(TM).