Fourier-Jacobi expansion and the Ikeda lift

2011 ◽  
Vol 81 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Shuichi Hayashida
Keyword(s):  
Jacobi Expansion ◽  
Ikeda Lift

Algebraic Constructions of Minimal Compactifications

2013 ◽  
Author(s):  
Kai-Wen Lan
Keyword(s):  
Large Class ◽  
Automorphic Forms ◽  
Algebraic Construction ◽  
Local Structures ◽  
Jacobi Expansion ◽  
Integral Bases ◽  
Toroidal Compactifications ◽  
Jacobi Expansions ◽  
Algebraic Constructions ◽  
Moduli Problems

This chapter first studies the automorphic forms that are defined as global sections of certain invertible sheaves on the toroidal compactifications. The local structures of toroidal compactifications lead naturally to the theory of Fourier–Jacobi expansions and the Fourier–Jacobi expansion principle. The chapter also obtains the algebraic construction of arithmetic minimal compactifications (of the coarse moduli associated with moduli problems), which are projective normal schemes defined over the same integral bases as the moduli problems are. As a by-product of codimension counting, we obtain Koecher's principle for arithmetic automorphic forms (of naive parallel weights). Furthermore, this chapter shows the projectivity of a large class of arithmetic toroidal compactifications by realizing them as normalizations of blowups of the corresponding minimal compactifications.

scholarly journals A remark on the Ikeda lift and local singular series polynomials

2007 ◽  
Vol 136 (05) ◽  
pp. 1559-1564 ◽  
Author(s):  
YoungJu Choie ◽  
Winfried Kohnen
Keyword(s):  
Singular Series ◽  
Ikeda Lift

On the period of the Ikeda lift for U(m, m)

2016 ◽  
Vol 286 (1-2) ◽  
pp. 141-178
Author(s):  
Hidenori Katsurada
Keyword(s):  
Ikeda Lift
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