Zeroes of zeta functions and symmetry

  title={Zeroes of zeta functions and symmetry},
  author={Nicholas M. Katz and Peter Sarnak},
  journal={Bulletin of the American Mathematical Society},
  • N. Katz, P. Sarnak
  • Published 1999
  • Mathematics
  • Bulletin of the American Mathematical Society
Hilbert and Polya suggested that there might be a natural spectral interpretation of the zeroes of the Riemann Zeta function. While at the time there was little evidence for this, today the evidence is quite convincing. Firstly, there are the “function field” analogues, that is zeta functions of curves over finite fields and their generalizations. For these a spectral interpretation for their zeroes exists in terms of eigenvalues of Frobenius on cohomology. Secondly, the developments, both… 

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