On the discriminant of pure number fields

Anuj Jakhar, Sudesh K. Khanduja, Neeraj Sangwan Colloquium Mathematicum MSC: 11R04, 11R29. DOI: 10.4064/cm8257-11-2020 Published online: 24 May 2021

Abstract

Let $K=\mathbb {Q}(\sqrt [n]{a})$ be an extension of degree $n$ of the field $\mathbb Q $ of rational numbers, where the integer $a$ is such that for each prime $p$ dividing $n$ either $p\nmid a$ or the highest power of $p$ dividing $a$ is coprime to $p$; this condition is clearly satisfied when $a, n$ are coprime or $a$ is squarefree. The paper contains an explicit formula for the discriminant of $K$ involving only the prime powers dividing $a,n$.

Authors

  • Anuj JakharDepartment of Mathematics
    Indian Institute of Technology Bhilai
    Raipur, 492015, India
    e-mail
  • Sudesh K. KhandujaIndian Institute of
    Science Education and Research Mohali
    Sector 81, Knowledge City
    SAS Nagar, Punjab 140306, India
    and
    Department of Mathematics
    Panjab University
    Chandigarh 160014, India
    e-mail
  • Neeraj SangwanDepartment of Mathematics
    Indian Institute of Technology (IIT) Bombay
    Mumbai 400076, India
    e-mail

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