TY - JOUR
T1 - On the modular forms of weight 1/2 over algebraic number fields
AU - Kojima, Hisashi
AU - Sakata, Hiroshi
N1 - Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/12
Y1 - 2021/12
N2 - Serre and Stark succeeded in deciding a basis of the space of modular forms of weight 1/2 over the rational number field. Achimescu and Saha generalized their result to the case of modular forms of weight 1/2 over totally real algebraic number fields. Gove also solved this problem in the case of modular forms of weight 1/2 over imaginary quadratic fields. In this paper, we determine an explicit basis of the space of modular forms of weight 1/2, level c and character ψ over algebraic number fields. We prove our assertion using their arguments and Shimura's transformation formula of theta series over algebraic number fields.
AB - Serre and Stark succeeded in deciding a basis of the space of modular forms of weight 1/2 over the rational number field. Achimescu and Saha generalized their result to the case of modular forms of weight 1/2 over totally real algebraic number fields. Gove also solved this problem in the case of modular forms of weight 1/2 over imaginary quadratic fields. In this paper, we determine an explicit basis of the space of modular forms of weight 1/2, level c and character ψ over algebraic number fields. We prove our assertion using their arguments and Shimura's transformation formula of theta series over algebraic number fields.
KW - Automorphic forms on GL(2)
KW - Forms of half-integer weight
KW - Theta series
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U2 - 10.1016/j.jnt.2021.04.009
DO - 10.1016/j.jnt.2021.04.009
M3 - Article
AN - SCOPUS:85109441114
VL - 229
SP - 364
EP - 385
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
ER -