### Abstract

The action of the derivation θ = q d/dq on the q-expansions of modular forms in characteristic p is one of the fundamental tools in the Serre/Swinnerton-Dyer theory of mod p modular forms. In this note, we extend the basic results about this action, already known for P ≥ 5 and level one, to arbitrary p and arbitrary prime-to-p level.

Original language | English (US) |
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Title of host publication | Modular Functions of one Variable V |

Subtitle of host publication | Proceedings International Conference, University of Bonn, Sonderforschungsbereich Theoretische Mathematik July 2-14, 1976 |

Publisher | Springer Verlag |

Pages | 53-61 |

Number of pages | 9 |

ISBN (Print) | 9783540083481 |

DOIs | |

State | Published - Aug 25 2006 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 601 |

ISSN (Print) | 0075-8434 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

Katz, N. M. (2006). A result on modular forms in characteristic p. In

*Modular Functions of one Variable V: Proceedings International Conference, University of Bonn, Sonderforschungsbereich Theoretische Mathematik July 2-14, 1976*(pp. 53-61). (Lecture Notes in Mathematics; Vol. 601). Springer Verlag. https://doi.org/10.1007/BFb0063944