A note on trigonometric polynomials for lower bounds of (s)

Non-negative trigonometric polynomials satisfying certain properties are employed when studying a number of aspects of the Riemann zeta function. When establishing zero-free regions in the critical strip, the classical polynomial 3+4 () + (2) used by de la Vall\'ee Poussin has since been replaced by more beneficial polynomials with larger degree. The classical polynomial was also employed by Titchmarsh to provide a lower bound on | (+it) | when >1. We show that this polynomial is optimal for this purpose.