TY - JOUR
T1 - Hecke operators on Drinfeld cusp forms
AU - Li, Wen Ching Winnie
AU - Meemark, Yotsanan
N1 - Funding Information:
✩ The research of the first author is supported in part by the NSF grant DMS-0457574. Part of the research was performed while she was visiting the National Center for Theoretical Sciences, Mathematics Division, in Hsinchu, Taiwan. She would like to thank the Center for its support and hospitality. The second author was supported in part by Grants for Development of New Faculty Staff from Chulalongkorn University, Thailand. * Corresponding author. E-mail addresses: [email protected] (W.-C.W. Li), [email protected] (Y. Meemark).
PY - 2008/7
Y1 - 2008/7
N2 - In this paper, we study the Drinfeld cusp forms for Γ1 (T) and Γ (T) using Teitelbaum's interpretation as harmonic cocycles. We obtain explicit eigenvalues of Hecke operators associated to degree one prime ideals acting on the cusp forms for Γ1 (T) of small weights and conclude that these Hecke operators are simultaneously diagonalizable. We also show that the Hecke operators are not diagonalizable in general for Γ1 (T) of large weights, and not for Γ (T) even of small weights. The Hecke eigenvalues on cusp forms for Γ (T) with small weights are determined and the eigenspaces characterized.
AB - In this paper, we study the Drinfeld cusp forms for Γ1 (T) and Γ (T) using Teitelbaum's interpretation as harmonic cocycles. We obtain explicit eigenvalues of Hecke operators associated to degree one prime ideals acting on the cusp forms for Γ1 (T) of small weights and conclude that these Hecke operators are simultaneously diagonalizable. We also show that the Hecke operators are not diagonalizable in general for Γ1 (T) of large weights, and not for Γ (T) even of small weights. The Hecke eigenvalues on cusp forms for Γ (T) with small weights are determined and the eigenspaces characterized.
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U2 - 10.1016/j.jnt.2008.02.008
DO - 10.1016/j.jnt.2008.02.008
M3 - Article
AN - SCOPUS:44349151728
SN - 0022-314X
VL - 128
SP - 1941
EP - 1965
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 7
ER -