Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Sarah Peluse"'
Publikováno v:
Forum of Mathematics, Sigma, Vol 12 (2024)
Let $P_1, \ldots , P_m \in \mathbb {K}[\mathrm {y}]$ be polynomials with distinct degrees, no constant terms and coefficients in a general local field $\mathbb {K}$ . We give a quantitative count of the number of polynomial progressions $x, x+P_
Externí odkaz:
https://doaj.org/article/587a36421de747288164c8dc69f3b4ea
Autor:
Sarah Peluse
Publikováno v:
Forum of Mathematics, Pi, Vol 8 (2020)
Let $P_1,\dots ,P_m\in \mathbb{Z} [y]$ be polynomials with distinct degrees, each having zero constant term. We show that any subset A of $\{1,\dots ,N\}$ with no nontrivial progressions of the form $x,x+P_1(y),\dots ,x+P_m(y)$ has size $|A|\ll N/(\l
Externí odkaz:
https://doaj.org/article/4da606ee384f43be9eb32bdfece35683
Autor:
Sarah Peluse
We show that the number of positive integers $n\leq N$ such that $\mathbb{Z}/(n^2+n+1)\mathbb{Z}$ contains a perfect difference set is asymptotically $N/\log{N}$.
Comment: 31 pages; v2: referee suggestions incorporated
Comment: 31 pages; v2: referee suggestions incorporated
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f6bc93277eef3d91831105897d702d99
Autor:
Sarah Peluse, Sean Prendiville
We show that sets of integers lacking the configuration $x$, $x+y$, $x+y^2$ have at most polylogarithmic density.
Comment: v2. Replaced use of Hahn-Banach theorem with simplified treatment involving Cauchy-Schwarz
Comment: v2. Replaced use of Hahn-Banach theorem with simplified treatment involving Cauchy-Schwarz
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a72234ab0e936e13f4c1e83c2a8c09db
Autor:
Sarah Peluse
Let $P_1,\dots,P_m\in\mathbb{Z}[y]$ be polynomials with distinct degrees, each having zero constant term. We show that any subset $A$ of $\{1,\dots,N\}$ with no nontrivial progressions of the form $x,x+P_1(y),\dots,x+P_m(y)$ has size $|A|\ll N/(\log\
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bd1b3fc299635b42cd041fa7c6f3eefb
http://arxiv.org/abs/1909.00309
http://arxiv.org/abs/1909.00309
Autor:
Sarah Peluse
Publikováno v:
Duke Math. J. 168, no. 5 (2019), 749-774
Let $P_1,\dots,P_m\in\mathbb{Z}[y]$ be any linearly independent polynomials with zero constant term. We show that there exists a $\gamma>0$ such that any subset of $\mathbb{F}_q$ of size at least $q^{1-\gamma}$ contains a nontrivial polynomial progre
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5f855f261a406f7511fcf22d0decad2e
https://doi.org/10.1215/00127094-2018-0051
https://doi.org/10.1215/00127094-2018-0051
Autor:
Sarah Peluse
Bourgain and Chang recently showed that any subset of $\mathbb{F}_p$ of density $\gg p^{-1/15}$ contains a nontrivial progression $x,x+y,x+y^2$. We answer a question of theirs by proving that if $P_1,P_2\in\mathbb{Z}[y]$ are linearly independent and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::81466a6b28f5cb02295970e1bb830c30
Autor:
Cornelia Mihaila, Thomas Garrity, Matthew Stoffregen, Nicholas Neumann-Chun, Krishna Dasaratha, Sarah Peluse, Chansoo Lee, Laure Flapan
Publikováno v:
Monatshefte für Mathematik. 174:549-566
We construct a countable family of multi-dimensional continued fraction algorithms, built out of five specific multidimensional continued fractions, and find a wide class of cubic irrational real numbers a so that either (a, a^2) or (a, a-a^2) is pur
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::da210577937d27f16d63b3adf45f2609
https://doi.org/10.1007/s00605-014-0643-1
https://doi.org/10.1007/s00605-014-0643-1
Autor:
Sarah Peluse
Publikováno v:
Archiv der Mathematik. 102:71-81
Eichler integrals play an integral part in the modular parametrizations of elliptic curves. In her master’s thesis, Kodgis conjectures several dozen zeros of Eichler integrals for elliptic curves with conductor ≤ 179. In this paper we prove a gen
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::625d02bb763243bc0135263b1a76865d
https://doi.org/10.1007/s00013-013-0602-4
https://doi.org/10.1007/s00013-013-0602-4
Publikováno v:
International Journal of Number Theory. :1563-1578
In his striking 1995 paper, Borcherds found an infinite product expansion for certain modular forms with CM divisors. In particular, this applies to the Hilbert class polynomial of discriminant $-d$ evaluated at the modular $j$-function. Among a numb
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::07e8fed547d6dc53c6ebdeb861a035da
https://doi.org/10.1142/s1793042113500437
https://doi.org/10.1142/s1793042113500437