On some properties of polynomials related to hypergeometric modular forms
type: Item
instance of: scholarly article
title: On some properties of polynomials related to hypergeometric modular forms
zbMATH Open document ID: 1121.33010
author: Masanobu Kaneko
author: Naruya Niiho
published in: The Ramanujan Journal
publication date: 2007-04-10T00:00:00Z
full work available at URL: http://hdl.handle.net/2324/20432
review text: The authors study certain polynomials \(P^{(r)}_m (x)\) with rational coefficients indexed by positive integers \(r,m\) with \(0\leq r \leq 5\). These polynomials are defined using hypergeometric series and have the property that the roots of their reductions mod \(p\) for certain specific primes \(p\) are related to the supersingular \(j\)-invariants in characteristic \(p\). The authors compute explicitly the discriminant of these polynomials and prove their irreducibility in certain cases. Finally they verify that the Galois group of \(P^{(r)}_m (x)\) over the rationals is the full symmetric group for all \(r\) and for \(m<150\).
reviewed by: Kartik Prasanna
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 11F11
zbMATH DE Number: 5141551
zbMATH Keywords: hypergeometric modular forms
zbMATH Keywords: supersingular j-invariants
zbMATH Keywords: orthogonal polynomials
MaRDI profile type: Publication
OpenAlex ID: W2015269718
cites work: Q4213385
cites work: Arithmetic of certain hypergeometric modular forms
cites work: Q4149801
DOI: 10.1007/S11139-006-0146-3
description: scientific article; zbMATH DE number 5141551