arXiv Open Access 2024

Quantitative concatenation for polynomial box norms

Noah Kravitz Borys Kuca James Leng

Lihat Sumber

Abstrak

Using PET and quantitative concatenation techniques, we establish box-norm control with the "expected" directions for counting operators for general multidimensional polynomial progressions, with at most polynomial losses in the parameters. Such results are often useful first steps towards obtaining explicit upper bounds on sets lacking instances of given such progressions. In the companion paper arXiv:2407.08637, we complete this program for sets in $[N]^2$ lacking nondegenerate progressions of the form $(x, y), (x + P(z), y), (x, y + P(z))$, where $P \in \mathbb{Z}[z]$ is any fixed polynomial with an integer root of multiplicity $1$.

Topik & Kata Kunci

math.CO math.NT

Penulis (3)

Noah Kravitz

Borys Kuca

James Leng

Format Sitasi

APA MLA BibTeX

Kravitz, N., Kuca, B., Leng, J. (2024). Quantitative concatenation for polynomial box norms. https://arxiv.org/abs/2407.08636

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓