Modular Forms with Integral Weight or Half-integral Weight

Xueli Wang () and Dingyi Pei ()
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Xueli Wang: South China Normal University, Department of Mathematics
Dingyi Pei: Guangzhou University, Institute of Mathematics and Information Science

Chapter Chapter 4 in Modular Forms with Integral and Half-Integral Weights, 2012, pp 65-88 from Springer

Abstract: Abstract Let Г be a Fuchsian group of the first kind. Then M = Г ∖ ℍ* is a compact Riemann surface. Denote by K the field of all meromorphic functions on M. It is well-known that K is an algebraic function field over ℂ Let ϕ: ℍ*→ M be the natural map. For g ∈ K we call f(z) = g(ϕ(z)) an automorphic function on ℍ which is a meromorphic function on ℍ. It is clear that f (γ(z)) = f(z) for any γ ∈ Г. Now we introduce a more wide range of functions on ℍ.

Date: 2012
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DOI: 10.1007/978-3-642-29302-3_4

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