Simon Leo Rydin Myerson

activity

20152025

most citedSystems of cubic forms in many variables

12 citations · 33 across the 13 of their papers we have counts for

collaborators

13 papers

math.AP2025

Bounds for spectral projectors on the three-dimensional torus

Pierre Germain, Simon L. Rydin Myerson, Daniel Pezzi

We study $L^{2}$ to $L^{p}$ operator norms of spectral projectors for the Euclidean Laplacian on the torus in the case where the spectral window is narrow. With a window of constant si…

math.NT2024

A two-dimensional delta symbol method and its application to pairs of quadratic forms

Junxian Li, Simon L. Rydin Myerson, Pankaj Vishe

We present a two-dimensional delta symbol method that facilitates a version of the Kloosterman refinement of the circle method, addressing a question posed by Heath-Brown. As an ap…

math.NT2024

Expander estimates for cubes

Joerg Bruedern, Simon L Rydin Myerson

If $A$ is a set of natural numbers of exponential density $δ$ , then the exponential density of all numbers of the form $x^{3} + a$ with $x \in N$ and $a \in A$ is…

math.NT2023

A question about points on an elliptic curve with prime denominator

Simon L Rydin Myerson

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(…

math.AP2022

Bounds for spectral projectors on generic tori

Pierre Germain, Simon L. Rydin Myerson

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 prov…

math.CA2022★ 1 cited

Bounds for spectral projectors on the Euclidean cylinder

Pierre Germain, Simon L. Rydin Myerson

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…

math.NT2021

Additive problems with almost prime squares

Valentin Blomer, Lasse Grimmelt, Junxian Li +1

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 r…

math.NT2021

The elliptic sieve and Brauer groups

Subham Bhakta, Daniel Loughran, Simon L. Rydin Myerson +1

A theorem of Serre states that almost all plane conics over $Q$ have no rational point. We prove an analogue of this for families of conics parametrised by elliptic curves…

math.AP2021★ 4 cited

Bounds for spectral projectors on tori

Pierre Germain, Simon Leo Rydin Myerson

We investigate norms of spectral projectors on thin spherical shells for the Laplacian on tori. This is closely related to the boundedness of resolvents of the Laplacian, and to th…

math.AP2018★ 5 cited

Strichartz estimates for the Schroedinger equation on non-rectangular two-dimensional tori

Yu Deng, Pierre Germain, Larry Guth +1

We propose a conjecture for long time Strichartz estimates on generic (non-rectangular) flat tori. We proceed to partially prove it in dimension 2. Our arguments involve on the one…

math.NT2017★ 9 cited

Systems of forms in many variables

Simon L. Rydin Myerson

We consider systems $F (x)$ of $R$ homogeneous forms of the same degree $d$ in $n$ variables with integral coefficients. If $n \geq d 2^{d} R + R$ and the coefficients of $\vec…

math.NT2017★ 12 cited

Systems of cubic forms in many variables

Simon L. Rydin Myerson

We consider a system of $R$ cubic forms in $n$ variables, with integer coefficients, which define a smooth complete intersection in projective space. Provided $n \geq 25 R$ , we prove…

math.NT2015★ 2 cited

Quadratic forms and systems of forms in many variables

Simon L. Rydin Myerson

Let $F_{1}, \dots, F_{R}$ be quadratic forms with integer coefficients in $n$ variables. When $n \geq 9 R$ and the variety $V (F_{1}, \dots, F_{R})$ is a smooth complete intersection, we prove…