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Determining Siegel modular forms of half-integral weight by their fundamental Fourier coefficients

Volume 195 / 2020

Abhash Kumar Jha Acta Arithmetica 195 (2020), 269-279 MSC: Primary 11F30, 11F46; Secondary 11F50. DOI: 10.4064/aa190308-22-1 Published online: 27 May 2020


We prove that a non-zero Siegel cusp form of half-integral weight and degree 2 on $\Gamma _0^{(2)}(4)$ has infinitely many non-zero Fourier coefficients indexed by semi-integral matrices having fundamental discriminant. This is the half-integral weight version of the result proved by A. Saha [Math. Ann. 355 (2013), 363–380] in the case of Siegel modular forms of integral weight and degree 2.


  • Abhash Kumar JhaDepartment of Mathematical Sciences
    IIT (BHU)
    Varanasi 221005, India

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