Arizona Winter School '13: Overconvergent Modular Functions Arizona Winter School '13: Overconvergent Modular Functions
Here is a web page with some information about my project for the 2013 Arizona Winter School. In particular, it will provide links to some of the papers referenced in the notes which are included below. The notes for the course together with the student projects can be found here:

Notes and Student Projects

Here is a diagram of the map X^rig_0(37) -> X^rig(1) together with the corresponding map of special fibres.

Some of the papers referenced in the text may be downloaded below; note that these papers are intended for reference only and should not be downloaded (or so my lawyers tell me):

  • Katz' Antwerp 1972 paper.

  • GouvĂȘa and Mazur on Families

  • Watson's paper on the Ramanujan congruences

  • Atkin and O'Brien on congruences

  • Loeffler's proof of the spectral conjecture for N=1 and p=2

  • My paper with Buzzard on slopes when N=1 and p=2

  • Coleman's original paper

  • Coleman's "small slope forms are classical"

  • Coleman on the explicit form of the canonical subgroup

  • Serre's elementary paper on p-adic modular forms

  • Serre's Bourbaki report on p-adic modular forms

  • Buzzard's Slope Conjectures

  • Buzzard's computer programmes

    For the ambitious, understanding OPAQUE would require at least understanding AQUE, and QUE, and QE, for the latter, see:

    Zelditch's survey on QE

    One might also want to know about measures on Berkovich spaces, for which one might want to consult

  • Baker and Rumely's book

  • Baker's 2007 AWS notes

    Also referenced in the text is

  • Conrad's notes

    Finally, to understand the relation of adjoint L-functions to ramification and pairings, one might take a look at:

  • Kim's Thesis