On calculations of the Fourier coefficients of cusp forms of half-integral weight given by the Shintani lift

Hisashi Kojima, Hiroshi Sakata*

*この研究の対応する著者

研究成果: Article査読

抄録

Shintani constructed the inverse mapping Ψ of Shimura correspondence Φ from a cusp form F(z) of half-integral weight to the cusp form f(z) of integral weight. The Fourier coefficients of the cusp form Ff(z) = Ψ (f(z)) are explicitly expressed in terms of periods of a cusp form f(z). Using the reduction theory of integral binary quadratic forms and calculations of periods of f(z), we shall decide an effective algorithm of a calculation of the Fourier coefficients of Ff(z) lifted by an cusp form f(z) of small level. Moreover, when f(z) is a cusp form of level 2 and of weight 8, we shall prove that Ff(z) is a certain product of some classical theta series of level 4 and of weight 1/2 and certain Dedekind eta functions.

本文言語English
ジャーナルIndian Journal of Pure and Applied Mathematics
DOI
出版ステータスAccepted/In press - 2023

ASJC Scopus subject areas

  • 数学一般
  • 応用数学

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