On Hecke modules generated by eta-products and imaginary quadratic fields
HTML articles powered by AMS MathViewer
- by Takeshi Ogasawara PDF
- Proc. Amer. Math. Soc. 145 (2017), 23-37 Request permission
Abstract:
We study two types of modules over the Hecke algebra generated by eta-products $\eta (\tau )\eta (N\tau )$ and $\eta (\tau )^3\eta (\lambda \tau )^3$ respectively. We give dimension formulas for them in terms of the class number of imaginary quadratic field.References
- Heng Huat Chan, Shaun Cooper, and Wen-Chin Liaw, On $\eta ^3(a\tau )\eta ^3(b\tau )$ with $a+b=8$, J. Aust. Math. Soc. 84 (2008), no. 3, 301–313. MR 2453682, DOI 10.1017/S144678870800058X
- Ernst Kani, Binary theta series and modular forms with complex multiplication, Int. J. Number Theory 10 (2014), no. 4, 1025–1042. MR 3208873, DOI 10.1142/S1793042114500134
- Günter Köhler, Eta products and theta series identities, Springer Monographs in Mathematics, Springer, Heidelberg, 2011. MR 2766155, DOI 10.1007/978-3-642-16152-0
- Gérard Ligozat, Courbes modulaires de genre $1$, Supplément au Bull. Soc. Math. France, Tome 103, no. 3, Société Mathématique de France, Paris, 1975 (French). Bull. Soc. Math. France, Mém. 43. MR 0417060
- Takeshi Ogasawara, A certain eta-quotient and the class number of an imaginary quadratic field, Int. J. Number Theory 10 (2014), no. 6, 1485–1499. MR 3248167, DOI 10.1142/S1793042114500390
- Kenneth A. Ribet, Galois representations attached to eigenforms with Nebentypus, Modular functions of one variable, V (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976) Lecture Notes in Math., Vol. 601, Springer, Berlin, 1977, pp. 17–51. MR 0453647
- B. Schoeneberg, Bemerkungen über einige Klassen von Modulformen, Nederl. Akad. Wetensch. Proc. Ser. A 70 = Indag. Math. 29 (1967), 177–182 (German). MR 0210674
Additional Information
- Takeshi Ogasawara
- Affiliation: Department of General Education, National Institute of Technology, Oyama College, 771 Nakakuki, Oyama City, Tochigi, 323-0806, Japan
- MR Author ID: 968234
- Email: t.ogasawara.4164@gmail.com
- Received by editor(s): March 3, 2016
- Published electronically: June 30, 2016
- Communicated by: Ken Ono
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 23-37
- MSC (2010): Primary 11F20; Secondary 11R29, 11F11
- DOI: https://doi.org/10.1090/proc/13186
- MathSciNet review: 3565357