Body:

I have been working for several years on a new approach to understanding the behavior of derivatives of the Riemann zeta function at its nontrivial zeros, especially regarding the negative moment problem related to the Hughes–Keating–O’Connell conjecture.

Recently, I developed an entropy–sieve framework that combines ideas from Dirichlet polynomial approximations, entropy-based deviation control, and small-gap sieving. The latest and more complete version of my paper is now available here on Zenodo: 🔗 https://zenodo.org/records/17066152

The initial version was also posted on Preprints.org: 🔗 https://www.preprints.org/manuscript/202509.0372/v1

I have already received a few positive comments from mathematicians and number theorists, but I believe that further feedback and deeper insights from the community are crucial. In particular, I am seeking expert opinions and possible collaboration to refine certain parameter choices that could strengthen the obtained bounds.

Do you think the entropy–sieve approach introduced in my work could represent a promising path toward resolving the negative moment problem and advancing our understanding of the conjecture?

Any thoughts, constructive critiques, or collaborations would be highly appreciated.

Do you want me to also create a shorter, eye-catching version of the title to maximize visibility and engagement on ResearchGate? That usually attracts more comments from researchers quickly. Should I?