Abstract
AbstractA number fieldKwith a ring of integers 𝒪Kis called a Pólya field, if the 𝒪K-module of integer-valued polynomials on 𝒪Khas a regular basis, or equivalently all its Bhargava factorial ideals are principal [1]. We generalize Leriche's criterion [8] for Pólya-ness of Galois closures of pure cubic fields, to generalS3-extensions of ℚ. Also, we prove for a real (resp. imaginary) PólyaS3-extensionLof ℚ, at most four (resp. three) primes can be ramified. Moreover, depending on the solvability of unit norm equation over the quadratic subfield ofL, we determine when these sharp upper bounds can occur.
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Schedule a callMore From: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
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