Abstract
Inspired by previous work of Bruinier-Ono and Mertens-Rolen, we study class polynomials for non-holomorphic modular functions arising from modular forms of negative weight.
In particular, we give general conditions for the irreducibility of class polynomials and obtain a general theorem to check when functions constructed in a special way are class invariants.
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Acknowledgements
This project was written at the Cologne Young Researchers in Number Theory Program 2015. The authors wish to thank the organizer Larry Rolen, for his generous support and guidance throughout the project. Furthermore, they want to recognize the generous support and contribution from the DFG Grant D-72133-G-403-151001011 of Larry Rolen, which was funded under the Institutional Strategy of the University of Cologne within the German Excellence Initiative. They would also like to thank Michael Griffin for insightful conversations. Further, the authors wish to express their gratitude to Claudia Alfes, Kathrin Bringmann, and Michael H. Mertens for their valuable comments and correspondence. Lastly, they would like to thank the anonymous referees for their helpful comments.
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Braun, J.J., Buck, J.J. & Girsch, J. Class invariants for certain non-holomorphic modular functions. Res. number theory 1, 21 (2015). https://doi.org/10.1007/s40993-015-0022-6
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DOI: https://doi.org/10.1007/s40993-015-0022-6