Lower bounds for moments of L-functions.

  title={Lower bounds for moments of L-functions.},
  author={Ze’ev Rudnick and K. Soundararajan},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  volume={102 19},
The moments of central values of families of L-functions have recently attracted much attention and, with the work of Keating and Snaith [(2000) Commun. Math. Phys. 214, 57-89 and 91-110], there are now precise conjectures for their limiting values. We develop a simple method to establish lower bounds of the conjectured order of magnitude for several such families of L-functions. As an example we work out the case of the family of all Dirichlet L-functions to a prime modulus. 
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The Theory of Riemann Zeta Function

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Multiplicative Number Theory (Springer, New York). 6838 www.pnas.org cgi doi 10.1073 pnas.0501723102 Rudnick and Soundararajan

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