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Abstract
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Khan, Milićević, and Ngo evaluated the second moment of
-functions
associated to certain Galois orbits of primitive Dirichlet
characters to modulus a large power of any fixed odd prime
. Their results
depend on
-adic
Diophantine approximation and are ineffective, in the sense of computability.
We obtain an effective asymptotic for this second moment in the case of
.
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Keywords
$L$-functions, Dirichlet characters, moments
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Mathematical Subject Classification 2010
Primary: 11M20
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Milestones
Received: 29 December 2017
Revised: 19 September 2018
Accepted: 12 October 2018
Published: 14 December 2018
Communicated by Stephan Garcia
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