Author ORCID Identifier
https://orcid.org/0009-0008-2781-7893
Date of Award
6-2026
Document Type
Thesis (Ph.D.)
Department or Program
Mathematics
First Advisor
John Voight
Second Advisor
Asher Auel
Abstract
We revisit Gauss composition over a general base scheme, with a focus on orthogonal groups. We show that the Clifford and norm functors provide a discriminant-preserving equivalence of categories between binary quadratic modules and pseudoregular modules over quadratic algebras. This perspective synthesizes the constructions of Kneser and Wood, reconciling algebraic and geometric approaches and clarifying the role of orientations and the natural emergence of narrow class groups.
As an application, we restrict to lattices and show that binary orthogonal eigenforms correspond to Hecke characters. Using theta series, we show the explicit connection between Hilbert modular forms and orthogonal modular forms arising from positive definite binary lattices over the ring of integers of a totally real number field.
Original Citation
John Voight and Haochen Wu, An orthogonal perspective on Gauss composition (2025). Available at https://arxiv.org/abs/2511.03987.
Recommended Citation
Wu, Haochen, "Gauss composition and orthogonal modular forms on binary lattices" (2026). Dartmouth College Ph.D Dissertations. 523.
https://digitalcommons.dartmouth.edu/dissertations/523
