Relative rank and regularization

DOI10.1017/fms.2024.15arXiv2106.03933OpenAlexW3167738070MaRDI QIDQ6193727

Tamar Ziegler, Amichai Lampert

Publication date: 19 March 2024

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.03933

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials over finite fields (11T06) Arithmetic combinatorics; higher degree uniformity (11B30)

Cites Work

• Diophantine equations in the primes
• Progression-free sets in \(\mathbb{Z}_4^n\) are exponentially small
• On large subsets of \(\mathbb{F}_q^n\) with no three-term arithmetic progression
• Linear forms and higher-degree uniformity for functions on \(\mathbb F^n_p\)
• Polynomial functions as splines
• Properties of high rank subvarieties of affine spaces
• The density of integer points on homogeneous varieties
• Polynomial bound for partition rank in terms of analytic rank
• Approximate cohomology
• The distribution of polynomials over finite fields, with applications to the Gowers norms
• An explicit version of Birch's Theorem
• Polynomial bound for the partition rank vs the analytic rank of tensors
• The analytic rank of tensors and its applications
• Small subalgebras of polynomial rings and Stillman’s Conjecture
• Structure vs. randomness for bilinear maps

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