Published paper
Abstract
The article establishes quantitative non-divergence for higher-dimensional algebraic trajectories on arithmetic homogeneous spaces and applies it to weak limits of translated algebraic measures.
Role in dependence graphs
Proof-critical source
The Dirichlet spectrum
This paper is included only for the following marked statements:
- Theorem 3.4 · GAFA 7 (1997), pp. 58–60Quantitative measure recurrence for the bounded exponential-polynomial trajectory class.
- Theorems 3.5 and 3.9 · GAFA 7 (1997), pp. 61–66Arithmetic parabolic alternative and the combined higher-rank non-divergence theorem.
- Proposition 3.7 · GAFA 7 (1997), pp. 61–63Reduction-theoretic compactness criterion inside Theorem 3.5.
AI-generated audit
Audit summary
Not a correctness certificate. These reports do not replace expert scrutiny or formal verification.
Exact reviewed source
Exact version of record hosted by an author · GAFA 7 (1997), 48–80
Alex Eskin, Shahar Mozes, and Nimish A. Shah. Non-divergence of translates of certain algebraic measures. Geometric and Functional Analysis 7 (1997), 48–80.
Open audited source ↗01Statements2 reported findingsNo statement issues found
The higher-dimensional non-divergence theorem and its arithmetic algebraic alternative are correctly stated.
Theorems 3.4 and 3.9No issue found
The compact-return alternative is uniform in the trajectory class
GAFA pages 58–66
Bounded exponential-polynomial complexity and bounded parameter-ball diameter are exactly the uniform data used to choose the compact set. The combined theorem gives either uniform contraction in a rational parabolic representation or return on a proportion at least one minus the prescribed error.
Proposition 3.7No issue found
The reduction-theoretic compact set is correctly identified
GAFA pages 61–63
The proposition is the image of Dani–Margulis Proposition 1.8 in the article's notation. Its compactness conclusion is precisely what is needed in the terminating step of Theorem 3.5.
02Proofs3 reported findingsNo proof issues found
The proof separates measure recurrence, algebraic reduction theory, and a finite induction on rational parabolic ranks. Each imported result is exact and the current published numbering is recorded.
Theorem 3.4No issue found in the reviewed proof
The Dani–Margulis proof transfers to the exponential-polynomial class
GAFA pages 58–60
The source proof uses only uniform one-variable polynomial small-value estimates. The paper proves those estimates for its larger function class, applies the one-dimensional result on radial slices, and covers larger balls by finitely many controlled smaller balls.
Theorem 3.5No issue found in the reviewed proof
The finite parabolic induction terminates
GAFA pages 61–65
Failure of uniform parabolic contraction supplies a lower bound for every relevant function. Proposition 3.8 either reaches a compact set immediately or enlarges the parabolic index set. Since its cardinality strictly increases, the construction stops after at most the rational rank.
Version mappingSource locator clarified
Shah's preprint locator maps to final Theorem 3.9
Final GAFA page 66
The earlier Shah paper refers to EMS Theorem 3.6 from a preprint. The final combined statement is Theorem 3.9, obtained from final Theorems 3.4 and 3.5.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.