World Scientific
  • Search
Skip main navigation

Cookies Notification

We use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at [email protected] for any enquiries.

On Siegel paramodular forms corresponding to skew-holomorphic Jacobi cusp forms by:1 (Source: Crossref)

    By extending arguments by Gritsenko, we construct a lifting of skew-holomorphic Jacobi cusp forms of odd weight k+1 and index N to Siegel paramodular forms of degree 2 with L2-integrability.

    AMSC: 11F46, 11F30, 11F37, 11F50


    • 1. T. M. Apostol , Introduction to Analytic Number Theory, Undergraduate Texts in Mathematics. (Springer-Verlag, New York, 1976). CrossrefGoogle Scholar
    • 2. K. Bringmann, A. Folsam, K. Ono and L. Rolen , Harmonic Maass Forms and Mock Modular Forms: Theory and Applications, American Mathematical Society Colloquium Publications, Vol. 64. (American Mathematical Society, Providence, RI, 2017). CrossrefGoogle Scholar
    • 3. M. Eichler and D. Zagier , The Theory of Jacobi Forms, Progress in Mathematics, Vol. 55 (Birkhäuser Boston, 1985). CrossrefGoogle Scholar
    • 4. A. Erdélyi , Transformation einer gewissen nach Produkten konfluenter hypergeometrischer Funktionen fortschreitenden Reihe, Compositio Math. 6 (1939) 336–347. Google Scholar
    • 5. V. Gritsenko , Arithmetical Lifting and its Applications, Number theory, London Mathematical Society Lecture Note Series, Vol. 215 (Cambridge University Press, Cambridge, 1995) pp. 103–126. CrossrefGoogle Scholar
    • 6. V. Gritsenko , Irrationality of the moduli spaces of polarized abelian surfaces, in Abelian varieties (de Gruyter, Berlin, 1995) pp. 63–81. CrossrefGoogle Scholar
    • 7. W. Kohnen , Jacobi forms and Siegel modular forms: recent results and problems, Enseign. Math. (2) 39 (1993) 121–136. Google Scholar
    • 8. W. Kohnen and Y. Martin , A characterization of degree two Siegel cusp forms by the growth of their Fourier coefficients, Forum Math. 26 (2014) 1323–1331. Crossref, Web of ScienceGoogle Scholar
    • 9. W. Magnus and F. Oberhettinger , Formeln und Sätze fÃ1 4r die speziellen Funktionen der mathematischen Physik, 2nd edn. (Springer-Verlag, Berlin, 1948). CrossrefGoogle Scholar
    • 10. T. Miyazaki , On Fourier-Jacobi expansions of real analytic Eisenstein series of degree 2, Abh. Math. Semin. Univ. Hambg. 84 (2014) 85–122. Crossref, Web of ScienceGoogle Scholar
    • 11. C. Mœglin and J.-L. Waldspurger , Spectral decomposition and Eisenstein series, in Une paraphrase de l’criture [A paraphrase of Scripture]. Cambridge Tracts in Mathematics, Vol. 113 (Cambridge University Press, Cambridge, 1995). CrossrefGoogle Scholar
    • 12. C. Poor and D. S. Yuen , The cusp structure of the paramodular groups for degree two, J. Korean Math. Soc. 50 (2013) 445–464. Crossref, Web of ScienceGoogle Scholar
    • 13. R. Schmidt , The Saito-Kurokawa lifting and functoriality, Amer. J. Math. 127 (2005) 209–240. Crossref, Web of ScienceGoogle Scholar
    • 14. R. Schmidt , Packet structure and paramodular forms, Trans. Amer. Math. Soc. 370 (2018) 3085–3112. Crossref, Web of ScienceGoogle Scholar
    • 15. G. Shimura , Confluent hypergeometric functions on tube domains, Math. Ann. 260 (1982) 269–302. Crossref, Web of ScienceGoogle Scholar
    • 16. G. Shimura , Invariant differential operators on Hermitian symmetric spaces, Ann. of Math. 132 (1990) 237–272. Crossref, Web of ScienceGoogle Scholar
    • 17. G. Shimura , Differential operators, holomorphic projection, and singular forms, Duke Math. J. 76 (1994) 141–173. Crossref, Web of ScienceGoogle Scholar
    • 18. G. Shimura , Euler Products and Eisenstein Series, CBMS Regional Conference Series in Mathematics, Vol. 93. (American Mathematical Society, Providence, RI, 1997). CrossrefGoogle Scholar
    • 19. G. Shimura , Arithmeticity in the Theory of Automorphic Forms, Mathematical Surveys and Monographs, Vol. 82 (American Mathematical Society, Providence, RI, 2000). Google Scholar
    • 20. G. Shimura, Collected papers, Vol. III. 1978–1988, Vol. IV. 1989–2001 (Springer-Verlag, New York, 2003). Google Scholar
    • 21. N.-P. Skoruppa , Developments in the theory of Jacobi forms, in Automorphic Functions and Their Applications, (Acad. Sci. USSR, Inst. Appl. Math., Khabarovsk, 1990) pp. 167–185. Google Scholar
    • 22. N.-P. Skoruppa , Binary quadratic forms and the Fourier coefficients of elliptic and Jacobi modular forms, J. Reine Angew. Math. 411 (1990) 66–95. Web of ScienceGoogle Scholar
    • 23. N. J. Vilenkin , Special Functions and the Theory of Group Representations, Translations of Mathematical Monographs, Vol. 22 (American Mathematical Society, Providence, RI, 1968). CrossrefGoogle Scholar