Pólya S3-extensions of ℚ
2018 ◽
Vol 149
(6)
◽
pp. 1421-1433
◽
Keyword(s):
AbstractA number field K with a ring of integers 𝒪K is called a Pólya field, if the 𝒪K-module of integer-valued polynomials on 𝒪K has 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 general S3-extensions of ℚ. Also, we prove for a real (resp. imaginary) Pólya S3-extension L of ℚ, at most four (resp. three) primes can be ramified. Moreover, depending on the solvability of unit norm equation over the quadratic subfield of L, we determine when these sharp upper bounds can occur.
1999 ◽
Vol 42
(1)
◽
pp. 127-141
Keyword(s):
2019 ◽
Vol 15
(10)
◽
pp. 1983-2025
Keyword(s):
2007 ◽
Vol 03
(04)
◽
pp. 541-556
◽
2018 ◽
Vol 14
(09)
◽
pp. 2333-2342
◽
2014 ◽
Vol 10
(04)
◽
pp. 885-903
◽
Keyword(s):
1988 ◽
Vol 111
◽
pp. 165-171
◽
Keyword(s):
2019 ◽
Vol 19
(04)
◽
pp. 2050080
Keyword(s):
2004 ◽
Vol 187
(1-3)
◽
pp. 169-182
◽