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Rational period functions and cycle integrals in higher level cases. (English) Zbl 1381.11029
Summary: Generalizing the results of W. Duke et al. [Abh. Math. Semin. Univ. Hamb. 80, No. 2, 255–264 (2010; Zbl 1269.11040)] we give an effective basis for the space of period polynomials in higher level cases and construct modular integrals for certain rational period functions related to indefinite binary quadratic forms by means of cycle integrals.

MSC:
11F11 Holomorphic modular forms of integral weight
11F03 Modular and automorphic functions
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[1] Buell, D., Binary quadratic forms, (1989), Springer
[2] Choi, S.; Kim, C. H., Congruences for Hecke eigenvalues in higher level cases, J. Number Theory, 131, 11, 2023-2036, (2011) · Zbl 1263.11055
[3] Choi, S.; Kim, C. H., Basis for the space of weakly holomorphic modular forms in higher level cases, J. Number Theory, 133, 1300-1311, (2013) · Zbl 1282.11027
[4] Choi, S.; Kim, C. H., Mock modular period functions and L-functions of cusp forms in higher level cases, Proc. Amer. Math. Soc., 142, 3369-3386, (2014) · Zbl 1305.11029
[5] Choie, Y.; Zagier, D., Rational period functions for \(\mathit{PSL}_2(\mathbb{Z})\), (Contemp. Math., vol. 143, (1993)), 89-108 · Zbl 0790.11044
[6] Duke, W.; Jenkins, P., On the zeros and coefficients of certain weakly holomorphic modular forms, Pure Appl. Math. Q., 4, 4, 1327-1340, (2008) · Zbl 1200.11027
[7] Duke, W.; Imamoḡlu, Ö.; Tóth, Á., Cycle integrals of the J-function and mock modular forms, Ann. of Math., 173, 2, 947-981, (2011) · Zbl 1270.11044
[8] Duke, W.; Imamoḡlu, Ö.; Tóth, Á., Rational period functions and cycle integrals, Abh. Math. Semin. Univ. Hambg., 80, 2, 255-264, (2010) · Zbl 1269.11040
[9] Gross, B.; Kohnen, W.; Zagier, D., Heegner points and derivatives of L-series, II, Math. Ann., 278, 497-562, (1987) · Zbl 0641.14013
[10] Kim, C. H., Borcherds products associated with certain Thompson series, Compos. Math., 140, 541-551, (2004) · Zbl 1059.11034
[11] Kim, C. H., Traces of singular moduli and borcherds products, Bull. Lond. Math. Soc., 38, 730-740, (2006) · Zbl 1120.11020
[12] Knopp, M., Some new results on the eichler cohomology of automorphic forms, Bull. Amer. Math. Soc., 80, 607-632, (1974) · Zbl 0292.10022
[13] Knopp, M., Rational period functions of the modular group, Duke Math. J., 45, 47-62, (1978) · Zbl 0374.10014
[14] Kohnen, W.; Zagier, D., Modular forms with rational periods, (Rankin, R. A., Modular Forms, (1984), Ellis Horwood), 197-249 · Zbl 0618.10019
[15] Miyake, T., Modular forms, (1989), Springer
[16] Shigezumi, J., On the zeros of certain poincare series for \(\operatorname{\Gamma}_0(2)\) and \(\operatorname{\Gamma}_0(3)\), Osaka J. Math., 47, 2, 487-505, (2010) · Zbl 1245.11051
[17] Zagier, D., Periods of modular forms, traces of Hecke operators and multiple zeta values, Sūrikaisekikenkyūsho Kōkyūroku, 843, 162-170, (1993)
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