The Size of the Lerch Zeta-Function at Places Symmetric with Respect to the Line ℜ(s) = 1/2

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 − s ¯ )| > | L ( λ , λ , s)|.