On Balanced Subgroups of the Multiplicative Group

Carl Pomerance, Douglas Ulmer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

A subgroup H of (ℤ/dℤ)× is called balanced if every coset of H is evenly distributed between the lower and upper halves of (ℤ/dℤ)×, i.e., has equal numbers of elements with representatives in (0,d/2) and (d/2,d). This notion has applications to ranks of elliptic curves. We give a simple criterion in terms of characters for a subgroup H to be balanced, and for a fixed integer p, we study the distribution of integers d such that the cyclic subgroup of (ℤ/dℤ)× generated by p is balanced.

Original languageEnglish (US)
Title of host publicationNumber Theory and Related Fields
Subtitle of host publicationIn Memory of Alf van der Poorten
PublisherSpringer New York LLC
Pages253-270
Number of pages18
ISBN (Print)9781461466413
DOIs
StatePublished - Jan 1 2013
Externally publishedYes

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume43
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Fingerprint

Multiplicative
Subgroup
Integer
Coset
Elliptic Curves
Character

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Pomerance, C., & Ulmer, D. (2013). On Balanced Subgroups of the Multiplicative Group. In Number Theory and Related Fields: In Memory of Alf van der Poorten (pp. 253-270). (Springer Proceedings in Mathematics and Statistics; Vol. 43). Springer New York LLC. https://doi.org/10.1007/978-1-4614-6642-0_14

On Balanced Subgroups of the Multiplicative Group. / Pomerance, Carl; Ulmer, Douglas.

Number Theory and Related Fields: In Memory of Alf van der Poorten. Springer New York LLC, 2013. p. 253-270 (Springer Proceedings in Mathematics and Statistics; Vol. 43).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Pomerance, C & Ulmer, D 2013, On Balanced Subgroups of the Multiplicative Group. in Number Theory and Related Fields: In Memory of Alf van der Poorten. Springer Proceedings in Mathematics and Statistics, vol. 43, Springer New York LLC, pp. 253-270. https://doi.org/10.1007/978-1-4614-6642-0_14
Pomerance C, Ulmer D. On Balanced Subgroups of the Multiplicative Group. In Number Theory and Related Fields: In Memory of Alf van der Poorten. Springer New York LLC. 2013. p. 253-270. (Springer Proceedings in Mathematics and Statistics). https://doi.org/10.1007/978-1-4614-6642-0_14
Pomerance, Carl ; Ulmer, Douglas. / On Balanced Subgroups of the Multiplicative Group. Number Theory and Related Fields: In Memory of Alf van der Poorten. Springer New York LLC, 2013. pp. 253-270 (Springer Proceedings in Mathematics and Statistics).
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