TY - GEN
T1 - Counting Monogenic Cubic Orders
AU - Akhtari, Shabnam
N1 - Funding Information:
I would like to thank Professor Manjul Bhargava who originally brought this topic to my attention. I would like to thank Professor Melvyn Nathanson for organizing Combinatorial and Additive Number Theory (CANT 2018) conference, and bringing together a truly diverse group of researchers. I would also like to acknowledge the support from the NSF grant DMS-1601837.
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020
Y1 - 2020
N2 - This article is an extension of the author’s talk at CANT 2018 conference. In a cubic number field K, we give an absolute upper bound for the number of monogenic orders which have small index compared to the discriminant of, the ring of integers of K. We will also show that a positive proportion of cubic number fields, when ordered by their discriminant, are not monogenic. We will not present any new proofs. We will rather rephrase some of the previous results of the author and collaborators in the language of cubic orders, after giving an overview of the subject. Our main results are stated in Sect. 5.
AB - This article is an extension of the author’s talk at CANT 2018 conference. In a cubic number field K, we give an absolute upper bound for the number of monogenic orders which have small index compared to the discriminant of, the ring of integers of K. We will also show that a positive proportion of cubic number fields, when ordered by their discriminant, are not monogenic. We will not present any new proofs. We will rather rephrase some of the previous results of the author and collaborators in the language of cubic orders, after giving an overview of the subject. Our main results are stated in Sect. 5.
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U2 - 10.1007/978-3-030-31106-3_2
DO - 10.1007/978-3-030-31106-3_2
M3 - Conference contribution
AN - SCOPUS:85076976720
SN - 9783030311056
T3 - Springer Proceedings in Mathematics and Statistics
SP - 13
EP - 24
BT - Combinatorial and Additive Number Theory III - CANT, 2017 and 2018
A2 - Nathanson, Melvyn B.
PB - Springer
T2 - 16th Workshops on Combinatorial and Additive Number Theory, CANT 2018
Y2 - 22 May 2018 through 25 May 2018
ER -