What question did this study set out to answer?

To provide sufficient conditions for the index of number fields associated with specific quadrinomials.

March 27, 2026

On Narkiewicz problem 22 for number fields associated with certain quadrinomials

TCTapas ChatterjeeIndian Institute of Technology Ropar KKKarishan KumarIndian Institute of Technology Ropar

Puntos clave

To provide sufficient conditions for the index of number fields associated with specific quadrinomials.
Defined the number field K corresponding to a minimal polynomial.
Established sufficient conditions for the index i(K) to equal 1 and 2.
Presented examples of infinite families of number fields for specified index values.
Identified conditions that allow i(K) to be 1 and 2.
Provided concrete examples illustrating infinite families of number fields with required index properties.

Resumen

Abstract Let K = Q (θ) K=Q () be a number field corresponding to the minimal polynomial f (x) = x n + ax n −1 + bx + c over the field Q Q, where θ is an algebraic integer. In this paper, we provide sufficient conditions for i (K) = 1 and i (K) = 2, which give a partial answer to the Narkiewicz Problem 22 for these number fields, where i (K) is the index of K. Finally, we provide examples of infinite families of number fields for which i (K) = 1 and i (K) = 2.

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