The fourth moment of derivatives of Dirichlet L-functions in function fields
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AbstractWe obtain the asymptotic main term of moments of arbitrary derivatives of L-functions in the function field setting. Specifically, we obtain the first, second, and mixed fourth moments. The average is taken over all non-trivial characters of a prime modulus $$Q \in {\mathbb {F}}_q [T]$$ Q ∈ F q [ T ] , and the asymptotic limit is as $${{\,\mathrm{deg}\,}}Q \longrightarrow \infty $$ deg Q ⟶ ∞ . This extends the work of Tamam who obtained the asymptotic main term of low moments of L-functions, without derivatives, in the function field setting. It is also the function field q-analogue of the work of Conrey, who obtained the fourth moment of derivatives of the Riemann zeta-function.
1988 ◽
Vol 39
(1)
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pp. 21-36
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2013 ◽
Vol 25
(2)
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pp. 285-305
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1988 ◽
Vol 28
(4)
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pp. 115-124
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2006 ◽
Vol 74
(3)
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pp. 461-470
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1999 ◽
Vol 60
(1)
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pp. 21-32
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2018 ◽
Vol 14
(02)
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pp. 371-382
2011 ◽
Vol 131
(10)
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pp. 1939-1961
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