The Size of the Lerch Zeta-Function at Places Symmetric with Respect to the Line ℜ(s) = 1/2
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Let ζ(s) be the Riemann zeta-function. If t ⩾ 6.8 and σ > 1/2, then it is known that the inequality |ζ(1 − s)| > |ζ(s)| is valid except at the zeros of ζ(s). Here we investigate the Lerch zeta-function L(λ, α, s) which usually has many zeros off the critical line and it is expected that these zeros are asymmetrically distributed with respect to the critical line. However, for equal parameters λ = α it is still possible to obtain a certain version of the inequality |L(λ, λ, \(1 - \bar s\))| > |L(λ, λ, s)|.
KeywordsLerch zeta-function functional equation zero distribution
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