• Title, Summary, Keyword: meromorphic modular form

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RAY CLASS INVARIANTS IN TERMS OF EXTENDED FORM CLASS GROUPS

  • Yoon, Dong Sung
    • 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.