Zobrazeno 1 - 10
of 163
pro vyhledávání: '"Sawin, Will"'
Autor:
Sawin, Will
We propose a refinement of the random matrix model for a certain family of $L$-functions over $\mathbb F_q[u]$, using techniques that we hope will eventually apply to an arbitrary family of $L$-functions. This consists of a probability distribution o
Externí odkaz:
http://arxiv.org/abs/2409.02876
We prove upper and lower bounds on the number of pairs of commuting $n\times n$ matrices with integer entries in $[-T,T]$, as $T\to \infty$. Our work uses Fourier analysis and leads us to an analysis of exponential sums involving matrices over finite
Externí odkaz:
http://arxiv.org/abs/2409.01920
Let $\Sigma_{g'}\to \Sigma_g$ be a cover of an orientable surface of genus g by an orientable surface of genus g', branched at n points, with Galois group H. Such a cover induces a virtual action of the mapping class group $\text{Mod}_{g,n+1}$ of a g
Externí odkaz:
http://arxiv.org/abs/2401.13906
Autor:
Kenyon, Richard, Kontsevich, Maxim, Ogievetsky, Oleg, Pohoata, Cosmin, Sawin, Will, Shlosman, Senya
For partially ordered sets $X$ we consider the square matrices $M^{X}$ with rows and columns indexed by linear extensions of the partial order on $X$. Each entry $\left( M^{X}\right)_{PQ}$ is a formal variable defined by a pedestal of the linear orde
Externí odkaz:
http://arxiv.org/abs/2401.05291
Autor:
Sawin, Will, Wood, Melanie Matchett
Cohen, Lenstra, and Martinet have given conjectures for the distribution of class groups of extensions of number fields, but Achter and Malle have given theoretical and numerical evidence that these conjectures are wrong regarding the Sylow $p$-subgr
Externí odkaz:
http://arxiv.org/abs/2301.00791
Autor:
Sawin, Will
Gilmer has recently shown that in any nonempty union-closed family $\mathcal F$ of subsets of a finite set, there exists an element contained in at least a proportion $.01$ of the sets of $\mathcal F$. We improve the proportion from $.01$ to $\frac{
Externí odkaz:
http://arxiv.org/abs/2211.11504
We establish the exact structure of the cohomology associated to a certain matrix exponential sum investigated in prior work (arXiv:2109.00762) of the first and last author.
Comment: 19 pages
Comment: 19 pages
Externí odkaz:
http://arxiv.org/abs/2210.07133
Autor:
Sawin, Will, Wood, Melanie Matchett
The moment problem in probability theory asks for criteria for when there exists a unique measure with a given tuple of moments. We study a variant of this problem for random objects in a category, where a moment is given by the average number of epi
Externí odkaz:
http://arxiv.org/abs/2210.06279
Autor:
Sawin, Will
We give an axiomatic characterization of multiple Dirichlet series over the function field $\mathbb F_q(T)$, generalizing a set of axioms given by Diaconu and Pasol. The key axiom, relating the coefficients at prime powers to sums of the coefficients
Externí odkaz:
http://arxiv.org/abs/2209.13072
Autor:
Sawin, Will
We study p-adic hyper-Kloosterman sums, a generalization of the Kloosterman sum with a parameter k that recovers the classical Kloosterman sum when k=2, over general p-adic rings and even equal characteristic local rings. These can be evaluated by a
Externí odkaz:
http://arxiv.org/abs/2209.02170