Zobrazeno 1 - 10
of 32
pro vyhledávání: '"Leng, James"'
Autor:
Leng, James, Sawhney, Mehtaab
Let $g$ be sufficiently large, $b\in\{0,\ldots,g-1\}$, and $\mathcal{S}_b$ be the set of integers with no digit equal to $b$ in their base $g$ expansion. We prove that every sufficiently large odd integer $N$ can be written as $p_1 + p_2 + p_3$ where
Externí odkaz:
http://arxiv.org/abs/2409.06894
A $P$-polynomial corner, for $P \in \mathbb{Z}[z]$ a polynomial, is a triple of points $(x,y),\; (x+P(z),y),\; (x,y+P(z))$ for $x,y,z \in \mathbb{Z}$. In the case where $P$ has an integer root of multiplicity $1$, we show that if $A \subseteq [N]^2$
Externí odkaz:
http://arxiv.org/abs/2407.08637
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 resu
Externí odkaz:
http://arxiv.org/abs/2407.08636
We prove quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm. The proof is modeled after work of Green, Tao, and Ziegler and uses as a crucial input recent work of the first author regarding the equidistribution of nilseque
Externí odkaz:
http://arxiv.org/abs/2402.17994
Let $r_k(N)$ denote the size of the largest subset of $[N] = \{1,\ldots,N\}$ with no $k$-term arithmetic progression. We show that for $k\ge 5$, there exists $c_k>0$ such that \[r_k(N)\ll N\exp(-(\log\log N)^{c_k}).\] Our proof is a consequence of re
Externí odkaz:
http://arxiv.org/abs/2402.17995
Let $r_5(N)$ be the largest cardinality of a set in $\{1,\ldots,N\}$ which does not contain $5$ elements in arithmetic progression. Then there exists a constant $c\in (0,1)$ such that \[r_5(N)\ll \frac{N}{\exp((\log\log N)^{c})}.\] Our work is a cons
Externí odkaz:
http://arxiv.org/abs/2312.10776
Autor:
Leng, James
We give improved bounds for the equidistribution of (multiparameter) nilsequences subject to any degree filtration. The bounds we obtain are single exponential in dimension, improving on double exponential bounds of Green and Tao. To obtain these bou
Externí odkaz:
http://arxiv.org/abs/2312.10772
Autor:
Leng, James
This is a companion paper to arXiv:2312.10772. We deduce an equidistribution theorem for periodic nilsequences and use this theorem to give two applications in arithmetic combinatorics. The first application is quasi-polynomial bounds for a certain c
Externí odkaz:
http://arxiv.org/abs/2306.13820
We prove a fractal uncertainty principle with exponent $\frac{d}{2} - \delta + \varepsilon$, $\varepsilon > 0$, for Ahlfors--David regular subsets of $\mathbb R^d$ with dimension $\delta$ which satisfy a suitable "nonorthogonality condition". This ge
Externí odkaz:
http://arxiv.org/abs/2302.11708
Autor:
Leng, James
We demonstrate that $$\|\mu\|_{U^3([N])} \ll_{A}^{\text{ineff}} \log^{-A}(N)$$ $$\|\Lambda - \Lambda_Q\|_{U^3([N])} \ll_{A}^{\text{ineff}} \log^{-A}(N)$$ for any $A > 0$ where $\Lambda_Q$ is an approximant to the von Mangoldt function and will be def
Externí odkaz:
http://arxiv.org/abs/2212.09635