Matching the Lens to the Zero

Abstract. A short note on the Li-Sekatskii coefficients: the one-parameter family of Li coefficients obtained by shifting the Mobius map, whose unit circle is the critical line for every admissible shift. The construction is Sekatskii's; what the note adds is that the shift behaves as a lens with an exact optimal width, so matching the lens to a hypothetical zero improves the detection index by a factor equal to its height. It also records a truncation artifact that manufactures a false detection, and includes a shorter derivation of the same optimum contributed by S. K. Sekatskii.