Asymptotic growth patterns for class field towers
Arindam Bhattacharyya
Chennai Mathematical Institute, Tamil Nadu, IndiaVishnu Kadiri
Chennai Mathematical Institute, Tamil Nadu, IndiaAnwesh Ray
Chennai Mathematical Institute, Tamil Nadu, India
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Abstract
Let be an odd prime number. We study growth patterns associated with finitely ramified Galois groups considered over the various number fields varying in a -tower. These Galois groups can be considered as non-commutative analogues of ray class groups. For certain -extensions in which a given prime above is completely split, we prove precise asymptotic lower bounds. Our investigations are motivated by the classical results of Iwasawa, who showed that there are growth patterns for -primary class numbers of the number fields in a -tower.
Cite this article
Arindam Bhattacharyya, Vishnu Kadiri, Anwesh Ray, Asymptotic growth patterns for class field towers. Doc. Math. 29 (2024), no. 1, pp. 141–158
DOI 10.4171/DM/949