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Title: | Derivatives of p-adic Siegel Eisenstein series and p-adic degrees of arithmetic cycles |

Authors: | Marks, Samuel |

Advisors: | Skinner, Christopher |

Department: | Mathematics |

Class Year: | 2019 |

Abstract: | Kudla has given for each $n\ge 1$ a genus $n$ weight $\tfrac{n + 1}{2}$ Siegel Eisenstein series with odd functional equation whose central derivative he speculates to have arithmetic content. Specifically, these {\it incoherent} Eisenstein series vanish at $s = 0$ and their derivatives are nonholomorphic modular forms whose Fourier coefficients seem be degrees of $0$-cycles on certain Shimura varieties. When $n$ is odd, we search for evidence of a $p$-adic analogue which relates the derivative of a $p$-adic Siegel Eisenstein series to $p$-adic degrees of $0$-cycles. Indeed, when $n = 1$ or $3$, we construct an analogous $p$-adic Siegel Eisenstein series, compute the Fourier expansion of its derivative, and relate the resulting Fourier coefficients to $p$-adic degrees of the same $0$-cycles studied by Kudla. |

URI: | http://arks.princeton.edu/ark:/88435/dsp01kw52jb91d |

Type of Material: | Princeton University Senior Theses |

Language: | en |

Appears in Collections: | Mathematics, 1934-2020 |

Files in This Item:

File | Description | Size | Format | |
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MARKS-SAMUEL-THESIS.pdf | 364.73 kB | Adobe PDF | Request a copy |

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