Item – Theses Canada

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OCLC number
434557374
Link(s) to full text
LAC copy
LAC copy
Author
Greenberg, Matthew,1978-
Title
Heegner points and rigid analytic modular forms.
Degree
Ph. D. -- McGill University, 2006
Publisher
Ottawa : Library and Archives Canada = Bibliothèque et Archives Canada, [2007]
Description
1 microfiche
Notes
Includes bibliographical references.
Abstract
In the first part of this thesis, building on ideas of R. Pollack and G. Stevens, we present an efficient algorithm for integrating certain rigid analytic functions attached to automorphic forms on definite quaternion algebras. We then apply these methods, in conjunction with the Jacquet-Langlands correspondence and the uniformization theorem of Cerednik-Drinfeld, to the computation ' p'-adic periods of and Heegner points on elliptic curves defined over <math> <f> <blkbd>Q</blkbd></f> </math> and <math> <f> <blkbd>Q<fen lp="par"><rad><rcd><rm>5</rm></rcd></rad><rp post="par"></fen> </blkbd></f> </math> which are uniformized by Shimura curves. In part two, we give a new proof of the result, originally proved in unpublished work of Glenn Stevens [27], that every modular eigensymbol of non-critical slope lifts uniquely to a rigid-analytic distribution-valued eigensymbol. The proof is algorithmic and facilitates the efficient calculation of certain ' p'-adic integrals. This has applications to the calculation of Stark-Heegner points on elliptic curves defined over <math> <f> <blkbd>Q</blkbd></f> </math> as well as over certain imaginary quadratic fields.
ISBN
9780494251584
0494251581