## Abstract

Let p be a prime number. Continuing and extending our previous paper with the same title, we prove explicit rates of overconvergence for modular functions of the form

where

is a classical, normalized Eisenstein series on

and V the p-adic Frobenius operator. In particular, we extend our previous paper to the primes 2 and 3. For these primes our main theorem improves somewhat upon earlier results by Emerton, Buzzard and Kilford, and Roe. We include a detailed discussion of those earlier results as seen from our perspective. We also give some improvements to our earlier paper for primes

. Apart from establishing these improvements, our main purpose here is also to show that all of these results can be obtained by a uniform method, i.e., a method where the main points in the argumentation is the same for all primes. We illustrate the results by some numerical examples.

where

is a classical, normalized Eisenstein series on

and V the p-adic Frobenius operator. In particular, we extend our previous paper to the primes 2 and 3. For these primes our main theorem improves somewhat upon earlier results by Emerton, Buzzard and Kilford, and Roe. We include a detailed discussion of those earlier results as seen from our perspective. We also give some improvements to our earlier paper for primes

. Apart from establishing these improvements, our main purpose here is also to show that all of these results can be obtained by a uniform method, i.e., a method where the main points in the argumentation is the same for all primes. We illustrate the results by some numerical examples.

Originalsprog | Engelsk |
---|---|

Artikelnummer | 4 |

Tidsskrift | Research in Number Theory |

Vol/bind | 10 |

Udgave nummer | 1 |

Sider (fra-til) | 1-14 |

ISSN | 2363-9555 |

DOI | |

Status | Udgivet - 2024 |