Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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RATIONAL PERIOD FUNCTIONS FOR Γ+0 (3) WITH POLES ONLY AT 0

  • SoYoung Choi (Department of Mathematics Education and RINS Gyeongsang National University)
  • Received : 2023.10.06
  • Accepted : 2023.11.13
  • Published : 2023.11.30
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Abstract

We characterize a rational period function q(z) for Γ+0 (3) which has a pole only at 0.

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References

  1. G. Bol, Invarianten linearer differentialgleichungen, Abh. Math. Sem. Univ. Hamburg., 16 (1949), nos. 3-4, 1-28.  https://doi.org/10.1007/BF03343515
  2. S. Choi and C. H. Kim, Rational period functions in higher level cases, J. Number Theory 157 (2015), 64-78.  https://doi.org/10.1016/j.jnt.2015.04.021
  3. Y. Choie and L. A. Parson, Rational period functions and indefinite quadratic forms I, Math. Ann., 286 (1990), no. 4, 697-707.  https://doi.org/10.1007/BF01453597
  4. Y. Choie and L. A. Parson, Rational period functions and indefinite quadratic forms II, Illinois J. Math., 35 (1991), no. 3, 374-400.  https://doi.org/10.1215/ijm/1255987785
  5. Y. Choie and D. Zagier, Rational period functions for P SL(2, ℤ), Contemp. Math., 143 (1993), 89-108.  https://doi.org/10.1090/conm/143/00992
  6. M. Knopp, Rational period functions of the modular group, Duke Math. J., 45 (1978), no. 1, 47-62.  https://doi.org/10.1215/S0012-7094-78-04504-0
  7. M. Knopp, Rational period functions of the modular group II, Glasgow Math. J., 22 (1981), no. 2, 185-197.  https://doi.org/10.1017/S0017089500004663
  8. D. Y. Oh, Rational period functions for Γ+0 (2) with poles only in ℚ ∪ {∞}, Proc. Japan Acad. Ser. A Math. Sci., 99 (2023), no. 1, 7-12. 
  9. L. A. Parson, Rational period functions and indefinite binary quadratic forms, III, Contemp. Math., 143 (1993), 109-116. https://doi.org/10.1090/conm/143/00993