A note on lower bounds for numerical series
arXiv:2512.09004
Abstract
After passage to the representing measure, the three principal theorems of Esstafa and Sfaxi, J. Math. Anal. Appl. 556 (2026), 130199, reduce respectively to Jensen's inequality, one quadratic identity, and a one-point measure. We solve the underlying reciprocal-moment problem sharply, determine all extremisers, and obtain a strictly stronger Hurwitz-zeta bound. We also identify the gap between formal inversion and evaluation at 1, and give explicit counterexamples to further analytic claims.
Comment on https://doi.org/10.1016/j.jmaa.2025.130199