Scholarlink

<p>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, <i>p</i>-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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(G_\mathbb {Q}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mi mathvariant="double-struck">Q</mi> </msub> </math></EquationSource> </InlineEquation> and the <i>L</i>-function of each extension coincides with the <i>L</i>-function of an automorphic form.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The explicit hypergeometric-modularity method II

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年10月30日

查看全文
  • Michael Allen,
  • Brian Grove,
  • Ling Long,
  • Fang-Ting Tu

摘要

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.