• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.293-314
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• 2012

We prove that the Siegel modular form of D'Hoker and Phong that gives the chiral superstring measure in degree two is a lift. This gives a fast algorithm for computing its Fourier coefficients. We prove a general lifting from Jacobi cusp forms of half integral index t/2 over the theta group ${\Gamma}_1$(1, 2) to Siegel modular cusp forms over certain subgroups ${\Gamma}^{para}$(t; 1, 2) of paramodular groups. The theta group lift given here is a modification of the Gritsenko lift.

• East Asian mathematical journal
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• v.37 no.1
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• pp.87-95
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• 2021

Let K be an imaginary quadratic field with ��K its ring of integers. For a positive integer N, let K(N) be the ray class field of K modulo N��K, and let ��N be the field of meromorphic modular functions of level N whose Fourier coefficients lie in the Nth cyclotomic field. For each h ∈ ��N, we construct a ray class invariant as its special value in terms of the extended form class group, and show that the invariant satisfies the natural transformation formula via the Artin map in the sense of Siegel and Stark. Finally, we establish an isomorphism between the extended form class group and Gal(K(N)/K) without any restriction on K.