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pro vyhledávání: '"Wooley, P."'
Autor:
Bruedern, Joerg, Wooley, Trevor D.
We provide new estimates for smooth Weyl sums on minor arcs and explore their consequences for the distribution of the fractional parts of $\alpha n^k$. In particular, when $k\ge 6$ and $\rho(k)$ is defined via the relation $\rho(k)^{-1}=k(\log k+8.0
Externí odkaz:
http://arxiv.org/abs/2408.06441
Let $(p_n)$ denote the sequence of prime numbers, with $2=p_1
Externí odkaz:
http://arxiv.org/abs/2406.19491
Autor:
Bruedern, Joerg, Wooley, Trevor D.
We survey the potential for progress in additive number theory arising from recent advances concerning major arc bounds associated with mean value estimates for smooth Weyl sums. We focus attention on the problem of representing large positive intege
Externí odkaz:
http://arxiv.org/abs/2402.09537
We investigate $k$-superirreducible polynomials, by which we mean irreducible polynomials that remain irreducible under any polynomial substitution of positive degree at most $k$. Let $\mathbb F$ be a finite field of characteristic $p$. We show that
Externí odkaz:
http://arxiv.org/abs/2309.15304
Autor:
Wooley, Trevor D.
Consider a set of integers $\mathscr A$ having finite diameter $X$, and a system of simultaneous polynomial equations to be solved over $\mathscr A$. In many circumstances, it is known that the number of solutions of this system is $O(X^\epsilon |\ma
Externí odkaz:
http://arxiv.org/abs/2305.19968
Autor:
Wooley, Trevor D.
Fix $k,s,n\in \mathbb N$, and consider non-zero integers $c_1,\ldots ,c_s$, not all of the same sign. Provided that $s\ge k(k+1)$, we establish a Hasse principle for the existence of lines having integral coordinates lying on the affine diagonal hype
Externí odkaz:
http://arxiv.org/abs/2305.05071
Autor:
Bruedern, Joerg, Wooley, Trevor D.
Let $k_i\in \mathbb N$ $(i\ge 1)$ satisfy $2\le k_1\le k_2\le \ldots $. Freiman's theorem shows that when $j\in \mathbb N$, there exists $s=s(j)\in \mathbb N$ such that all large integers $n$ are represented in the form $n=x_1^{k_j}+x_2^{k_{j+1}}+\ld
Externí odkaz:
http://arxiv.org/abs/2302.12920
Autor:
Chase Wooley, BS, Daniel B. Maselli, MD, Lauren L. Donnangelo, MD, Areebah Waseem, BS, Shannon Casey, MSc, Brian Coan, MD, Christopher E. McGowan, MD
Publikováno v:
VideoGIE, Vol 9, Iss 7, Pp 317-319 (2024)
Externí odkaz:
https://doaj.org/article/117f0f4e37424761bf9e8d174ce60a08
Autor:
Wooley, Trevor D.
For every finite abelian group $G$, there are positive integers $n$ and $d$ such that $G$ is isomorphic to the multiplicative group of $d$-th powers of reduced residues modulo $n$.
Comment: 3 pages
Comment: 3 pages
Externí odkaz:
http://arxiv.org/abs/2211.10520
Autor:
Wooley, Trevor D.
Let $\varphi_1,\ldots ,\varphi_r\in \mathbb Z[z_1,\ldots z_k]$ be integral linear combinations of elementary symmetric polynomials with $\text{deg}(\varphi_j)=k_j$ $(1\le j\le r)$, where $1\le k_1
Externí odkaz:
http://arxiv.org/abs/2211.10500