The explicit hypergeometric-modularity method II
Michael W. Allen, Brian Grove, Ling Long, Fang-Ting Tu · Research in the Mathematical Sciences · 2025
Abstract In the first paper of this sequence, Allen et al (Adv. Math 478:110411, 2025), we provided an explicit hypergeometric modularity method by combining different techniques from the classical, p -adic, and finite field settings. In this article, we explore an application of this method from a motivic viewpoint through some known hypergeometric well-poised formulae of Whipple and McCarthy. Using well-poised hypergeometric formulae we construct a class of degree four Galois representations of corresponding cyclotomic fields. These representations are then shown to be extendable to the full absolute Galois group $$G_\mathbb {Q}$$ G Q and the L -function of each extension coincides with the L -function of an automorphic form.