The point of this note is to prove that the secrecy function attains its maximum at y = 1 on all known extremal even unimodular lattices. This is a special case of a conjecture by Belfiore and Solé. Further, we will give a very simple method to verify or disprove the conjecture on any given unimodular lattice.

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We define modified Li coefficients, called τ -Li coefficients for a very broad class S (σ 0 , σ 1 ) of L-functions that contains the Selberg class, the class of all automorphic L-functions and the Rankin-Selberg L-functions, as well as products of suitable shifts of those functions. We prove the generalized Li criterion for zero-free regions of functions belonging to the class S (σ 0 , σ 1 ), derive an arithmetic formula for the computation of τ -Li coefficients and conduct numerical investigation of τ -Li coefficients for a certain product of shifts of the Riemann zeta function. .fi (A.-M. Ernvall-Hytönen), almasa@pmf.unsa.ba (A. Odžak), lejlas@pmf.unsa.ba (L. Smajlović), medina.susic@pmf.unsa.ba (M. Sušić).

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