Andrew Pendleton

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math.NT2026

Multiplicities of eigenvalues and quadratic representations of integers

Siqi Fu, Andrew Pendleton

We study the set $M$ of all multiplicities of non-zero eigenvalues for the Laplace operator on a two-dimensional rectangle or torus. We show that for a rectangle with the side leng…

math.NT2025

Improved Bounds for the Index Conjecture in Zero-Sum Theory

Andrew Pendleton

The Index Conjecture in zero-sum theory states that when $n$ is coprime to $6$ and $k$ equals $4$ , every minimal zero-sum sequence of length $k$ modulo $n$ has index $1$ . While oth…