Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01kw52jb91d
 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