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pro vyhledávání: '"Thompson, Lola"'
Let $s(n)$ denote the sum of proper divisors of an integer $n$. In 1992, Erd\H{o}s, Granville, Pomerance, and Spiro (EGPS) conjectured that if $\mathcal{A}$ is a set of integers with asymptotic density zero then $s^{-1}(\mathcal{A})$ also has asympto
Externí odkaz:
http://arxiv.org/abs/2307.12859
Autor:
Helfgott, Harald A., Thompson, Lola
We present a new elementary algorithm that takes \[ \mathrm{time} \ \ O_\epsilon\left(x^{\frac{3}{5}} (\log x)^{\frac{3}{5}+\epsilon} \right) \ \ \mathrm{and}\ \ \mathrm{space} \ \ O\left(x^{\frac{3}{10}} (\log x)^{\frac{13}{10}} \right)\] for comput
Externí odkaz:
http://arxiv.org/abs/2101.08773
It is known that the lengths of closed geodesics of an arithmetic hyperbolic orbifold are related to Salem numbers. We initiate a quantitative study of this phenomenon. We show that any non-compact arithmetic $3$-dimensional orbifold defines $c Q^{1/
Externí odkaz:
http://arxiv.org/abs/2001.07851
Autor:
Thompson, Lola
This book presents new research on the leading edge of neurochemistry. Chapter One provides recent developments in understanding the neurochemistry of endogenous sulfur-containing amino acids as neuromodulators, metabolic intermediates and potential
Publikováno v:
Mathematika 64 (2018) 330-342
Let $s(\cdot)$ denote the sum-of-proper-divisors function, that is, $s(n) = \sum_{d\mid n,~d
Externí odkaz:
http://arxiv.org/abs/1706.03120
Publikováno v:
C. R. Math. Acad. Sci. Paris 355 (2017), 1121-1126
In 1992, Reid asked whether hyperbolic 3-manifolds with the same geodesic length spectra are necessarily commensurable. While this is known to be true for arithmetic hyperbolic 3-manifolds, the non-arithmetic case is still open. Building towards a ne
Externí odkaz:
http://arxiv.org/abs/1705.08034
Autor:
Akhtari, Shabnam, Aktaş, Kevser, Biggs, Kirsti, Hamieh, Alia, Petersen, Kathleen, Thompson, Lola
The goal of this paper is to obtain lower bounds on the height of an algebraic number in a relative setting, extending previous work of Amoroso and Masser. Specifically, in our first theorem we obtain an effective bound for the height of an algebraic
Externí odkaz:
http://arxiv.org/abs/1704.02995
Autor:
Schwab, Nicholas, Thompson, Lola
A positive integer $n$ is practical if every $m \leq n$ can be written as a sum of distinct divisors of $n$. One can generalize the concept of practical numbers by applying an arithmetic function $f$ to each of the divisors of $n$ and asking whether
Externí odkaz:
http://arxiv.org/abs/1701.08504
A positive integer $n$ is called $\varphi$-practical if the polynomial $X^n-1$ has a divisor in $\mathbb{Z}[X]$ of every degree up to $n$. In this paper, we show that the count of $\varphi$-practical numbers in $[1, x]$ is asymptotic to $C x/\log x$
Externí odkaz:
http://arxiv.org/abs/1511.03357
Publikováno v:
Math. Res. Lett. 24 (2017), 1497-1522
Our main result is that for all sufficiently large $x_0>0$, the set of commensurability classes of arithmetic hyperbolic 2- or 3-orbifolds with fixed invariant trace field $k$ and systole bounded below by $x_0$ has density one within the set of all c
Externí odkaz:
http://arxiv.org/abs/1504.05257