Average values of L-series for real characters in function fields
Andrade, JC; Bae, S; Jung, H
Date: 2 November 2016
Journal
Research in the Mathematical Sciences
Publisher
SpringerOpen
Publisher DOI
Abstract
We establish asymptotic formulae for the first and second moments of quadratic
Dirichlet L–functions, at the centre of the critical strip, associated to the real
quadratic function field k(
√
P) and inert imaginary quadratic function field k(
√
γP) with
P being a monic irreducible polynomial over a fixed finite field Fq of odd ...
We establish asymptotic formulae for the first and second moments of quadratic
Dirichlet L–functions, at the centre of the critical strip, associated to the real
quadratic function field k(
√
P) and inert imaginary quadratic function field k(
√
γP) with
P being a monic irreducible polynomial over a fixed finite field Fq of odd cardinality q
and γ a generator of F
×
q . We also study mean values for the class number and for the
cardinality of the second K-group of maximal order of the associated fields for ramified
imaginary, real, and inert imaginary quadratic function fields over Fq.
One of the main novelties of this paper is that we compute the second moment of
quadratic Dirichlet L-functions associated to monic irreducible polynomials. It is worth
noting that the similar second moment over number fields is unknown.
The second innovation of this paper comes from the fact that, if the cardinality of the
ground field is even then the task of average L-functions in function fields is much harder
and, in this paper, we are able to handle this strenuous case and establish several mean
values results of L-functions over function fields.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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