Acta Mathematica Sinica

, Volume 11, Issue 2, pp 200–210 | Cite as

Theta function and hilbert modular forms of half integral weight

  • Feng Xuning 


In this paper a kind of theta function is constructed by means of spherical function. And we also obtain some Hilbert modular forms of half integral weight.


Modular Form Theta Function Spherical Function Integral Weight Half Integral Weight 
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  1. [1]
    Feng Xuning,An analog of η(z) in the Hilbert modular case, J. Number Theory,17:1(1983), 116–126.Google Scholar
  2. [2]
    Hecke, E., Lectures on the theory of algebraic numbers (Translated from German), Springer-Verlag, 1981, 196–200.Google Scholar
  3. [3]
    Goro Shimura,On modular forms of half integral weight, Annals of Mathematics,97:3(1973), 440–481.Google Scholar
  4. [4]
    Stein, E. M. & Weiss, G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, 155, 1971.Google Scholar

Copyright information

© Science Press 1995

Authors and Affiliations

  • Feng Xuning 
    • 1
  1. 1.Institute of MathematicsAcademia SinicaBeijingPeople's Republic of China

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