the Cup Product's Applications To Ebisu's Method

Abstract

In [Ebisu2017], Akihito Ebisu found a remarkable new method to derive certain identities for hypergeometric functions, those identities are known as special values. Ebisu's method involves the use of so-called contiguity relations between hypergeometric functions. In this thesis, we study Ebisu's method and give an alternative approach using cup product relations. This alternative approach gives rise to a more insightful way to do the calculations. With these new insights, we try to answer questions, such as how many special values there exist and what there is beyond the values Ebisu applied his method to in [Ebisu2017].