Matthew C. Welsh

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20182023

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

1 citations · 2 across the 5 of their papers we have counts for

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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.NT2021★ 1 cited

Fine-scale distribution of roots of quadratic congruences

Jens Marklof, Matthew Welsh

We establish limit laws for the distribution in small intervals of the roots of the quadratic congruence $μ^{2} \equiv D mod m$ , with $D > 0$ square-free and $D\not\equiv 1 \bmod 4…

math.NT2020

Parameterizing roots of polynomial congruences

Matthew Welsh

We use the arithmetic of ideals in orders to parameterize the roots $μ (mod m)$ of the polynomial congruence $F (μ) \equiv 0 (mod m)$ , $F (X) \in Z [X]$ monic, irreducible and…

math.NT2018★ 1 cited

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