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OP-11915Status unassessedNumber theory

Geometric zero-sum criteria in finite-field vector spaces

Geometric zero-sum criteria in finite-field vector spaces. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

MSC 11 · Number theory

Editorial MSC2020 mapping of Geometric zero-sum criteria in finite-field vector spaces. https://ems.press/content/serial-article-files/52435#page=57 Not an author-supplied code.

Source question · editorial summaryAs of 2025; current status unassessedSource & evidence ↓
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Problem statement

Find a natural geometric condition on a set of p+n−1p+n-1 points in Fpn\mathbb F_p^n ensuring a nonempty zero-sum subset. The intended generalization is the plane criterion for p+1p+1 points, one on each line through the origin, discussed in the source.

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Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

References
  1. [1]Problem-session contributors; compiled by Thomas F. Bloom. Oberwolfach 2025 — Analytic Number Theory Problem Session (2025).; Geometric zero-sum criteria in finite-field vector spaces linkCC BY-SA 4.0; source contributors, compiled by Thomas F. Bloom. These attributed adaptations are available under the same license.

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