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A. Speiser proved that the Riemann hypothesis is equivalent to the absence ofnon-real zeros of the derivative of the Riemann zeta-function left of thecritical line. His result has been extended by N. Levinson and H.L. Montgomeryto the statement that the Riemann zeta-function and its derivative haveapproximately the same number of non-real zeros left of the critical line. Weobtain the Levinson-Montgomery type result for the Lerch zeta-function withequal parameters. For the Lerch zeta-function, the analogue of the Riemannhypothesis is usually not true and its zeros usually are distributedasymmetrically with respect to the critical line. However, for equalparameters, the symmetry of the zeros is almost restored.

Zeros of the Lerch zeta-function and of its derivative for equal parameters