ALGEBRAIC INTEGERS AS SPECIAL VALUES OF MODULAR UNITS

Cited 2 time in webofscience Cited 0 time in scopus
  • Hit : 338
  • Download : 1029
Let phi(tau) = eta(1/2(tau + 1))(2) / root 2 pi exp{1/4 pi i}eta(tau + 1), where eta(tau) is the Dedekind eta function. We show that if tau(0) is an imaginary quadratic argument and m is an odd integer, then root m phi(m tau(0))/phi(tau(0)) is an algebraic integer dividing root m. This is a generalization of a result of Berndt, Chan and Zhang. On the other hand, when K is an imaginary quadratic field and theta(K) is an element of K with lm(theta(K)) > 0 which generates the ring of integers of K over Z, we find a sufficient condition on in which ensures that root m phi(m theta(K))/phi(theta(K)) is a unit.
Publisher
CAMBRIDGE UNIV PRESS
Issue Date
2012-02
Language
English
Article Type
Article
Citation

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v.55, pp.167 - 179

ISSN
0013-0915
DOI
10.1017/S0013091510001094
URI
http://hdl.handle.net/10203/97368
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
000299661500010.pdf(192.48 kB)Download
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 2 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0