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On Critical Values of L-Functions for Holomorphic Forms on GSp(4) X GL(2)


Saha, Abhishek (2009) On Critical Values of L-Functions for Holomorphic Forms on GSp(4) X GL(2). Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5HWD-TH76.


Let F be a genus two Siegel newform and g a classical newform, both of squarefree levels and of equal weight ℓ. We derive an explicit integral representation for the degree eight L-function L(s, F x g). As an application, we prove a reciprocity law --- predicted by Deligne's conjecture --- for the critical special values L(m, F x g) where m ∈ Z, 2 ≤ m ≤ ℓ/2 -1. The proof of our integral representation has two major components: the generalization of an earlier integral representation due to Furusawa and a ``pullback formula" relating the complicated Eisenstein series of Furusawa with a simpler one on a higher rank group. The critical value result follows from our integral representation using rationality results of Garrett and Harris and the theory of nearly holomorphic forms due to Shimura.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:automorphic forms; critical values; Deligne's conjecture; integral representation; L-functions; siegel modular
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Scott Russell Johnson Graduate Dissertation Prize in Mathematics, 2009. Scott Russell Johnson Prize for Excellence in Graduate Study in Mathematics, 2005-2006.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Ramakrishnan, Dinakar
Thesis Committee:
  • Ramakrishnan, Dinakar (chair)
  • Balasubramaniam, Baskar
  • Mantovan, Elena
  • Flach, Matthias
Defense Date:11 May 2009
Non-Caltech Author Email:abhishek.saha (AT)
Record Number:CaltechETD:etd-05222009-162600
Persistent URL:
Saha, Abhishek0000-0002-2867-0386
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1964
Deposited By: Imported from ETD-db
Deposited On:29 May 2009
Last Modified:26 Nov 2019 20:23

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