Matthew C. Welsh

collaborators

3 papers

math.NT2023

Bounds for theta sums in higher rank II

Jens Marklof, Matthew Welsh

In the first paper of this series we established new upper bounds for multi-variable exponential sums associated with a quadratic form. The present study shows that if one adds a l…

math.NT2023

Geometry and distribution of roots of $μ^{2} \equiv D mod m$ with $D \equiv 1 mod 4$

Zonglin Li, Matthew Welsh

We extend the geometric interpretation of the roots of the quadratic congruence $μ^{2} \equiv D (mod m)$ as the tops of certain geodesics in the hyperbolic plane to the case when $D$ …

math.NT2018

Spacing and A Large Sieve Type Inequality for Roots of a Cubic Congruence

Matthew C. Welsh

Motivated by a desire to understand the distribution of roots of cubic congruences, we re-derive a parametrization of roots $ν (mod m)$ of $X^{3} \equiv 2 (mod m)$ found by Hooley. Al…

Bounds for theta sums in higher rank II

Geometry and distribution of roots of μ2≡Dmodm with D≡1mod4

Spacing and A Large Sieve Type Inequality for Roots of a Cubic Congruence

Geometry and distribution of roots of $μ^{2} \equiv D mod m$ with $D \equiv 1 mod 4$