* uschian groups of the first kind * Automorphic forms and functions * Hecke operators and the zeta-functions associated with modular forms * Elliptic curves * Abelian extensions of imaginary quadratic fields and complex multiplication of elliptic curves * Modular functions of higher level * Zeta-functions of algebraic curves and abelian varieties * The cohomology group assoicated with cusp forms * Arithmetic Fuschian groups

Introduction to the arithmetic theory of automorphic functions

Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.

Arithmetic duality theorems

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Introduction To Cyclotomic Fields

Journal of Algebra

基於Google Cloud Platform設計高效能日誌分析平台之研究

We describe the construction of a database of genus- curves of small discriminant that includes geometric and arithmetic invariants of each curve, its Jacobian, and the associated -function. This data has been incorporated into the -Functions and Modular Forms Database (LMFDB).

/pdf/a-database-of-genus-2-curves-over-the-rational-numbers-391g6p9rog.pdf

A database of genus-2 curves over the rational numbers

https://works.bepress.com/paul_gunnells/45/download/

On the cohomology of linear groups over imaginary quadratic fields

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 subcones, which descend give rise to hyperbolic tessellations of 3-dimensional hyperbolic space by ideal polytopes. 
We compute the structure of these polytopes for a range of imaginary quadratic fields.

Hyperbolic tessellations associated to Bianchi groups

Let F be the cubic field of discriminant –23 and let be its ring of integers. By explicitly computing cohomology of congruence subgroups of , we computationally investigate modularity of elliptic curves over F.

/pdf/modular-forms-and-elliptic-curves-over-the-cubic-field-of-1eil9wmg36.pdf

Modular forms and elliptic curves over the cubic field of discriminant –23

Let F/ℚ be a 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 subcones. In the case of an imaginary quadratic field these subcones descend to hyperbolic space to give rise to tessellations of 3-dimensional hyperbolic space by ideal polytopes. We compute the structure of these polytopes for a range of imaginary quadratic fields.

http://www.uncg.edu/mat/faculty/d_yasaki/publications/bianchipolytope.pdf

Dan Yasaki

Papers

A database of genus-2 curves over the rational numbers

On the cohomology of linear groups over imaginary quadratic fields

Hyperbolic tessellations associated to Bianchi groups

Modular forms and elliptic curves over the cubic field of discriminant –23

Hyperbolic Tessellations Associated to Bianchi Groups