Mean values of derivatives of L-functions in function fields: I
Journal of Mathematical Analysis and Applications
Reason for embargo
We investigate the first moment of the second derivative of quadratic Dirichlet L-functions over the rational function field. We establish an asymptotic formula when the cardinality of the finite field is fixed and the genus of the hyperelliptic curves associated to a family of Dirichlet L-functions over Fq(T) tends to infinity. As a more general result, we compute the full degree three polynomial in the asymptotic expansion of the first moment of the second derivative of this particular family of L-functions.
This research was partially supported by EPSRC grant EP/K021132X/1.
This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.
Available online 24 May 2016
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