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pro vyhledávání: '"Myerson, Simon L Rydin"'
If $\mathscr A$ is a set of natural numbers of exponential density $\delta$, then the exponential density of all numbers of the form $x^3+a$ with $x\in\mathbb N$ and $a\in\mathscr A$ is at least $\min(1, \frac 13+\frac 56 \delta)$. This is a consider
Externí odkaz:
http://arxiv.org/abs/2409.16795
Autor:
Myerson, Simon L Rydin
Let E be an elliptic curve defined by a Weierstrass equation with integer coefficients. Any rational point on E other than the identity is of the form $ ( x(P) / z(P)^2 , y(P) / z(P)^3 ) $ where $ x(P), y(P) \in \mathbb Z $ and $ z(P) \in \mathbb N $
Externí odkaz:
http://arxiv.org/abs/2307.09406
We investigate norms of spectral projectors on thin spherical shells for the Laplacian on generic tori, including generic rectangular tori. We state a conjecture and partially prove it, improving on previous results concerning arbitrary tori.
Co
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Externí odkaz:
http://arxiv.org/abs/2207.02967
We prove essentially optimal bounds for norms of spectral projectors on thin spherical shells for the Laplacian on the cylinder (R/Z)*R. In contrast to previous investigations into spectral projectors on tori, having one unbounded dimension available
Externí odkaz:
http://arxiv.org/abs/2203.08273
We show that every sufficiently large integer is a sum of a prime and two almost prime squares, and also a sum of a smooth number and two almost prime squares. The number of such representations is of the expected order of magnitude. We likewise trea
Externí odkaz:
http://arxiv.org/abs/2111.01601
A theorem of Serre states that almost all plane conics over $\mathbb{Q}$ have no rational point. We prove an analogue of this for families of conics parametrised by elliptic curves using elliptic divisibility sequences and a version of the Selberg si
Externí odkaz:
http://arxiv.org/abs/2109.03746
Autor:
Myerson, Simon L. Rydin
We consider systems $\vec{F}(\vec{x})$ of $R$ homogeneous forms of the same degree $d$ in $n$ variables with integral coefficients. If $n\geq d2^dR+R$ and the coefficients of $\vec{F}$ lie in an explicit Zariski open set, we give a nonsingular Hasse
Externí odkaz:
http://arxiv.org/abs/1709.08917
Autor:
Myerson, Simon L. Rydin
Let $F_1,\dotsc,F_R$ be quadratic forms with integer coefficients in $n$ variables. When $n\geq 9R$ and the variety $V(F_1,\dotsc,F_R)$ is a smooth complete intersection, we prove an asymptotic formula for the number of integer points in an expanding
Externí odkaz:
http://arxiv.org/abs/1512.06003
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Publikováno v:
Bhakta, S, Loughran, D, Rydin Myerson, S & Nakahara, M 2023, ' The elliptic sieve and Brauer groups ', Proceedings of the London Mathematical Society, vol. 126, no. 6, pp. 1884-1922 . https://doi.org/10.1112/plms.12520
A theorem of Serre states that almost all plane conics over $\mathbb{Q}$ have no rational point. We prove an analogue of this for families of conics parametrised by elliptic curves using elliptic divisibility sequences and a version of the Selberg si
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1e57caa5416e6049a4b61df44be18875
https://purehost.bath.ac.uk/ws/files/277342316/2109.03746.pdf
https://purehost.bath.ac.uk/ws/files/277342316/2109.03746.pdf