The Highest Lowest Zero

to appear in the Duke Mathematical Journal

  Stephen D. Miller

May 16, 1999

The Riemann Zeta Function's first zero is about 1/2+14.13472i.  Does any other L-function go as far without vanishing?

Why is the discrete spectrum of the laplacian on SL(68,Z)\SL(68,R)/SO(68,R) different than on lower-rank quotients?

We apply the positivity method of Stark-Odlyzko-Serre-Poitou-Mestre et al to these and other problems about automorphic forms on SL(n,Z)\SL(n,R)/SO(n,R).

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