2 citations · 3 across the 5 of their papers we have counts for
6 papers
An inverse problem on eigenfunction triple products
Carl Schildkraut, Romain Speciel
On a connected closed smooth Riemannian manifold, the algebraic structure of the Laplace eigenfunctions, as described by eigenfunction triple products, uniquely determines the geom…
Equiangular lines and large multiplicity of fixed second eigenvalue
Carl Schildkraut
Answering a question of Jiang and Polyanskii as well as Jiang, Tidor, Yao, Zhang, and Zhao, we show the existence of infinitely many angles for which the maximum number of line…
Graphs with high second eigenvalue multiplicity
Milan Haiman, Carl Schildkraut, Shengtong Zhang +1
Jiang, Tidor, Yao, Zhang, and Zhao recently showed that connected bounded degree graphs have sublinear second eigenvalue multiplicity (always referring to the adjacency matrix). Th…
On a Mertens-type conjecture for number fields
Daniel Hu, Ikuya Kaneko, Spencer Martin +1
We introduce a number field analogue of the Mertens conjecture and demonstrate its falsity for all but finitely many number fields of any given degree. We establish the existence o…
Order of Zeros of Dedekind Zeta Functions
Daniel Hu, Ikuya Kaneko, Spencer Martin +1
Answering a question of Browkin, we provide a new unconditional proof that the Dedekind zeta function of a number field has infinitely many nontrivial zeros of multiplicity at…
Pair Correlations in Uniform Countable Sets
Sanjay Raman, Carl Schildkraut
We determine the pair correlations of countable sets satisfying natural equidistribution conditions. The pair correlations are computed as the volume of a…