scholarly journals Construction of half integral weight Siegel modular forms of Sp (2, R) from automorphic forms of the compact twist Sp (2).

1985 ◽  
Vol 1985 (359) ◽  
pp. 188-220
Keyword(s):  
Modular Forms ◽  
Automorphic Forms ◽  
Siegel Modular Forms ◽  
Half Integral Weight ◽  
Integral Weight

scholarly journals Construction of siegel modular forms of degree three and commutation relations of Hecke operators

1985 ◽  
Vol 100 ◽  
pp. 83-96 ◽  
Author(s):  
Yoshio Tanigawa
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Siegel Modular Forms ◽  
Hecke Operators ◽  
Weil Representation ◽  
Commutation Relations ◽  
Half Integral Weight ◽  
Integral Weight ◽  
Shimura Correspondence

In connection with the Shimura correspondence, Shintani [6] and Niwa [4] constructed a modular form by the integral with the theta kernel arising from the Weil representation. They treated the group Sp(1) × O(2, 1). Using the special isomorphism of O(2, 1) onto SL(2), Shintani constructed a modular form of half-integral weight from that of integral weight. We can write symbolically his case as “O(2, 1)→ Sp(1)” Then Niwa’s case is “Sp(l)→ O(2, 1)”, that is from the halfintegral to the integral. Their methods are generalized by many authors. In particular, Niwa’s are fully extended by Rallis-Schiffmann to “Sp(l)→O(p, q)”.

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