On some arithmetic properties of Siegel functions

Cited 25 time in webofscience Cited 0 time in scopus
  • Hit : 323
  • Download : 3
We deal with several arithmetic properties of the Siegel functions which are modular units. By modifying the ideas in Kubert and Lang (Modular Units. Grundlehren der mathematischen Wissenschaften, vol 244. Spinger, Heidelberg, 1981), we establish certain criterion for determining a product of Siegel functions to be integral over Z[j]. We also find generators of the function fields K(X(1)(N)) by examining the orders of Siegel functions at the cusps and apply them to evaluate the Ramanujan's cubic continued fraction systematically. Furthermore we construct ray class invariants over imaginary quadratic fields in terms of singular values of j and Siegel functions.
Publisher
SPRINGER
Issue Date
2010-01
Language
English
Article Type
Article
Keywords

FORMULAS

Citation

MATHEMATISCHE ZEITSCHRIFT, v.264, no.1, pp.137 - 177

ISSN
0025-5874
DOI
10.1007/s00209-008-0456-9
URI
http://hdl.handle.net/10203/96547
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 25 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0