Statistics
for low-lying zeros of symmetric power L-functions in the level aspect
Published in Forum
Mathematicum 23, 969—1028 (2011).
Submitted
on 26 March 2007.
In
this paper, we compute the one-level density and the two-level density for
low-lying zeros of some families of symmetric power L-functions in the level
aspect. These families are built according to the value of the sign of the
functional equation. As a consequence, we completely determine the symmetry
types of these families.
The
main technical ingredients are some large sieve inequalities for Kloosterman sums and Riemann-von Mangoldt’s
explicit formula.
We
also compute the moments of the one-level density and produces
a new instance for Hughes-Rudnick’s mock Gaussian behaviour. This result relies
on heavy combinatorial arguments.
lowlyingprint.pdf lowlyingview.pdf
The previous texts are
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