On Balanced Subgroups of the Multiplicative Group

Carl Pomerance, Douglas Ulmer

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

5 Scopus citations


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
Number of pages18
ISBN (Print)9781461466413
StatePublished - 2013

Publication series

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

ASJC Scopus subject areas

  • Mathematics(all)


Dive into the research topics of 'On Balanced Subgroups of the Multiplicative Group'. Together they form a unique fingerprint.

Cite this