Moments of L-functions — Moments of the Riemann zeta function — Problem 32

Definitions and mathematical statement

The supplied record identifies Problem 32 in the section on moments of the Riemann zeta function of the problem list attributed to Hamieh, Kadiri, and Ng (2024). Its complete supplied mathematical request is:

Improve the range of $h$ and the size of the error term.

The parameter $h$ is not defined in the supplied record. The moment expression, underlying estimate, existing admissible range of $h$, and existing error bound are also absent. Consequently, neither the domain and quantifiers for $h$ nor the precise improvement sought can be specified from the supplied evidence. This request requires its missing mathematical context before it can be formulated as a standalone quantified problem.

Short English statement

The problem asks for a wider admissible range of an unspecified parameter $h$ and a better error bound in an unspecified result concerning moments of the Riemann zeta function. The supplied record lacks the definitions and baseline estimate needed to make these improvements precise.

Sources

• Local UnsolvedMath registry: permanent ID $800181$, source problem code catalogue entry, title "Moments of L-functions --- Moments of the Riemann zeta function --- Problem 32." The registry attributes the proposal to Hamieh, Kadiri, and Ng, with proposed year 2024, and labels its status as open. This is a supplied status label, not an independently verified mathematical assessment.
• Supplied source attribution: Hamieh, Kadiri, and Ng, Moments of L-functions Problem List (2024), Problem 32, https://arxiv.org/abs/2405.17800. The record reports access on 2026-10-16 and extraction by arxiv_latex; these are supplied provenance details, not a claim of independent source consultation or verification.