12 citations · 33 across the 13 of their papers we have counts for
8 papers · 1 filter
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…
Expander estimates for cubes
Joerg Bruedern, Simon L Rydin Myerson
If is a set of natural numbers of exponential density , then the exponential density of all numbers of the form with and is…
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(…
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…
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 have no rational point. We prove an analogue of this for families of conics parametrised by elliptic curves…
Systems of forms in many variables
Simon L. Rydin Myerson
We consider systems of homogeneous forms of the same degree in variables with integral coefficients. If and the coefficients of $\vec…
Systems of cubic forms in many variables
Simon L. Rydin Myerson
We consider a system of cubic forms in variables, with integer coefficients, which define a smooth complete intersection in projective space. Provided , we prove…
Quadratic forms and systems of forms in many variables
Simon L. Rydin Myerson
Let be quadratic forms with integer coefficients in variables. When and the variety is a smooth complete intersection, we prove…