50 citations · 86 across the 25 of their papers we have counts for
21 papers · 1 filter
Ternary Perfect Forms Over Imaginary Quadratic Field
Zachary Parker, Dan Yasaki
In this work, we enumerate the ternary perfect forms over all imaginary quadratic fields of absolute discriminant up to and study the number and combinatorial types of their a…
Bianchi Modular Forms over Imaginary Quadratic Fields with arbitrary class group
John Cremona, Kalani Thalagoda, Dan Yasaki
Let be an imaginary quadratic field and let be its ring of integers. For an integral ideal of , let be the c…
On the cohomology of GL_2 and SL_2 over imaginary quadratic fields
Herbert Gangl, Paul E. Gunnells, Jonathan Hanke +1
We report on computations of the cohomology of GL_2(O_D) and SL_2(O_D), where D<0 is a fundamental discriminant. These computations go well beyond earlier results of Vogtmann and S…
Cohomology of congruence subgroups of SL_3(Z), Steinberg modules, and real quadratic fields
Avner Ash, Dan Yasaki
We investigate the homology of a congruence subgroup Gamma of SL_3(Z) with coefficients in the Steinberg modules St(Q^3) and St(E^3), where E is a real quadratic field and the coef…
Perfect Forms over Imaginary Quadratic Fields
Kristen Scheckelhoff, Kalani Thalagoda, Dan Yasaki
In this work, we compute the perfect forms for all imaginary quadratic fields of absolute discriminant up to and study the number and types of the polytopes that arise. We p…
Steinberg homology, modular forms, and real quadratic fields
Avner Ash, Dan Yasaki
We compare the homology of a congruence subgroup Gamma of GL_2(Z) with coefficients in the Steinberg modules over Q and over E, where E is a real quadratic field. If R is any commu…
On the cohomology of congruence subgroups of GL3 over the Eisenstein integers
Paul E. Gunnells, Mark McConnell, Dan Yasaki
Let F be the imaginary quadratic field of discriminant -3 and OF its ring of integers. Let Gamma be the arithmetic group GL_3 (OF), and for any ideal n subset OF let Gamma_0 (n) be…
On the growth of torsion in the cohomology of arithmetic groups
Avner Ash, Paul E. Gunnells, Mark McConnell +1
Let G be a semisimple Lie group with associated symmetric space D, and let Gamma subset G be a cocompact arithmetic group. Let L be a lattice inside a Z Gamma-module arising from a…
A database of genus 2 curves over the rational numbers
Andrew R. Booker, Jeroen Sijsling, Andrew V. Sutherland +2
We describe the construction of a database of genus 2 curves of small discriminant that includes geometric and arithmetic invariants of each curve, its Jacobian, and the associated…
A table of elliptic curves over the cubic field of discriminant -23
Steve Donnelly, Paul E. Gunnells, Ariah Klages-Mundt +1
Let F be the cubic field of discriminant -23 and O its ring of integers. Let Gamma be the arithmetic group GL_2 (O), and for any ideal n subset O let Gamma_0 (n) be the congruence…
On the cohomology of linear groups over imaginary quadratic fields
Herbert Gangl, Paul E. Gunnells, Jonathan Hanke +3
Let Gamma be the group GL_N (OO_D), where OO_D is the ring of integers in the imaginary quadratic field with discriminant D<0. In this paper we investigate the cohomology of Gamma…
Modular forms and elliptic curves over the cubic field of discriminant -23
Paul E. Gunnells, Dan Yasaki
Let F be the cubic field of discriminant -23 and let O be its ring of integers. By explicitly computing cohomology of congruence subgroups of GL(2,O), we computationally investigat…
Modular forms and elliptic curves over the field of fifth roots of unity
Paul E. Gunnells, Farshid Hajir, Dan Yasaki
Let F be the cyclotomic field of fifth roots of unity. We computationally investigate modularity of elliptic curves over F.
Perfect forms over totally real number fields
Paul E. Gunnells, Dan Yasaki
A rational positive-definite quadratic form is perfect if it can be reconstructed from the knowledge of its minimal nonzero value m and the finite set of integral vectors v such th…
Hyperbolic tessellations associated to Bianchi groups
Dan Yasaki
Let F/Q be number field. The space of positive definite binary Hermitian forms over F form an open cone in a real vector space. There is a natural decomposition of this cone into s…
Binary Hermitian forms over a cyclotomic field
Dan Yasaki
Let z be a primitive fifth root of unity and let F be the cyclotomic field F=Q(z). Let O be the ring of integers. We compute the Voronoi polyhedron of binary Hermitian forms over F…
Hecke operators and Hilbert modular forms
Paul E. Gunnells, Dan Yasaki
Let F be a real quadratic field with ring of integers O and with class number 1. Let Gamma be a congruence subgroup of GL_2 (O). We describe a technique to compute the action of th…
Integral cohomology of certain Picard modular surfaces
Dan Yasaki
Let Gamma be a congruence subgroup of the Picard modular group of an imaginary number field k, and let D be the associated symmetric space. We describe a method to compute the inte…
The elliptic fixed points of the Picard modular group over the Gaussian integers
Dan Yasaki
We explicitly compute the ellitpic points and isotropy groups for the action of the Picard modular group over the Gaussian integers on 2-dimensional complex hyperbolic space.
On the existence of spines for Q-rank 1 groups
Dan Yasaki
Let X=Gamma\G/K be an arithmetic quotient of a symmetric space of non-compact type. In the case that G has Q-rank 1, we construct Gamma-equivariant deformation retractions of D=G/K…
Explicit reduction theory for SU(2,1;Z[i])
Dan Yasaki
Let Gamma\D be an arithmetic quotient of a symmetric space of non-compact type. A spine D_0 is a Gamma-equivariant deformation retraction of D with dimension equal to the virtual c…