Hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions

In this paper, we investigate the relationships among hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions through some families of `hypergeometric' algebraic varieties that are higher dimensional analogues of Legendre curves.Comment: 25 page

Computing Special LL-Values of Certain Modular Forms with Complex Multiplication

In this expository paper, we illustrate two explicit methods which lead to special $L$-values of certain modular forms admitting complex multiplication (CM), motivated in part by properties of $L$-functions obtained from Calabi-Yau manifolds defined over $\mathbb Q$

Generalized Legendre curves and Quaternionic Multiplication

This paper is devoted to abelian varieties arising from generalized Legendre curves. In particular, we consider their corresponding Galois representations, periods, and endomorphism algebras. For certain one parameter families of 2-dimensional abelian varieties of this kind, we determine when the endomorphism algebra of each fiber defined over the algebraic closure of $\Bbb Q$ contains a quaternion algebra