Margulis 1989 indefinite quadratic forms unipotent flows

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theorem_1_e0496_companion: Margulis Theorem 1 and a complete all-positive-integer deduction for positive irrational parameters.

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Source

G. A. Margulis, Indefinite quadratic forms and unipotent flows on homogeneous spaces, Banach Center Publications 23 (1989), 399–409. DOI: 10.4064/-23-1-399-409.

The complete 11-page primary PDF is margulis_1989_indefinite_quadratic_forms_unipotent_flows.pdf. The title page and the statement and reduction on printed pp. 399–400 were read for this extraction. The remaining dynamical proof has not been fully reconstructed here. The scan is image-only and its rendered first and last pages show no copyright or license line (its first page's header reads "PWN - Polish Scientific Publishers, Warszawa 1989"); the publisher's record offers the PDF under the download link "Pobierz zgodnie z CC-BY", rendered "Free download under CC-BY license" on the English site, and names no version or URL for it (https://www.impan.pl/get/doi/10.4064/-23-1-399-409, read 2026-10-02): the Creative Commons Attribution license, with no version stated.

Extracted result and proof obligation

theorem_1_e0496_companion states Theorem 1 on p. 399 with its exact nondegeneracy, indefiniteness, dimension, irrationality, and nonzero-vector hypotheses. It supplies a complete elementary deduction for the positive-parameter, all-positive-integer variant of E0496. The complete proof of Margulis's theorem, beginning with the reduction on p. 400 and continuing through its homogeneous-dynamics argument, remains ordinary source-proof compilation work. The deduction does not substitute for that proof.

Distinct 1989 source

This paper is distinct from Discrete Subgroups and Ergodic Theory, in Number Theory, Trace Formulas and Discrete Groups (Oslo 1987), 1989, pp. 377–398, DOI: 10.1016/B978-0-12-067570-8.50029-9, the chapter cited by the bibliography label [Ma89]. The exact Oslo chapter has not been obtained; no page, theorem, or full-proof claim is assigned to it. Access to this complete Banach Center paper does not discharge that separate acquisition gap.

Ji's 2008 survey is secondary corroboration of the general theorem and history, not a substitute primary source or an internal lemma of this paper.

Related formulations

The historical integer formulations appear in conjecture_p239. That companion explains the missing sign and nontriviality qualifications.