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math.NT2025
The Local-Global Conjecture is False for Generalized Circle Packings
Hanqi Shi, Wenyuan Shi, Ian Whitehead +2
Haag, Kertzer, Rickards, and Stange disprove the Local-Global Conjecture for Apollonian circle packings. We extend their disproof to four more types of integral circle packing: the…
math.NT2025
Functional equations of axiomatic multiple Dirichlet series, Weyl groupoids, and quantum algebra
Will Sawin, Ian Whitehead
We prove functional equations for multiple Dirichlet series defined by a collection of five geometric axioms. We find functional equations of two types: one modeled on the function…