Moments

Antanas Laurinčikas and Ramūnas Garunkštis
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Antanas Laurinčikas: Vilnius University
Ramūnas Garunkštis: Vilnius University

Chapter Chapter 3 in The Lerch Zeta-function, 2003, pp 31-51 from Springer

Abstract: Abstract In this chapter we will consider the classical mean value of L(λ, α, s) ∫ T 0 T | L ( λ , α , σ + i t ) | 2 d t , $$\int_{{T_0}}^T {{{\left| {L\left( {\lambda ,\alpha ,\sigma + it} \right)} \right|}^2}} dt,$$ and also the mean square with respect to α I ( λ , s ) = ∫ 0 1 | L ( λ , α , s ) − α − s | 2 d α . $$I\left( {\lambda ,s} \right) = {\int_0^1 {\left| {L\left( {\lambda ,\alpha ,s} \right) - {\alpha ^{ - s}}} \right|} ^2}d\alpha .$$

Keywords: Asymptotic Expansion; Explicit Formula; Residue Theorem; Dirichlet Polynomial; Approximate Functional Equation (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-6401-8_3

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DOI: 10.1007/978-94-017-6401-8_3

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