Published June 2012
| public
Journal Article
Determination of cusp forms on GL(2) by coefficients restricted to quadratic subfields (with an appendix by Dipendra Prasad and Dinakar Ramakrishnan)
- Creators
- Krishnamurthy, M.
Abstract
Given E/F a quadratic extension of number fields and a cuspidal representation π of GL_2(A_E), we give a full description of the fibers of the Asai transfer of π. We then determine the extent to which Fourier coefficients defined by integral ideals of F determine the representation π.
Additional Information
Published by Elsevier 2012. Received 29 August 2011, Accepted 20 September 2011, Available online 22 February 2012. Communicated by James W. Cogdell. This paper has an interesting history. An earlier draft of this paper was submitted for publication in the Shaidi volume on 14 May 2008 and was accepted for publication on August 1, 2008. However, due to some purely technical reasons, it was not included in the volume which came out in print in June, 2011. In the meantime (April, 2011 to be precise), Diprendra Prasad pointed out to the author that Dinakar Ramakrishna's cuspidality criterion [17, 16] is incomplete in the dihedral case. Since then, both Diprendra Prasad and Dinakar Ramakrishnan have given different proofs of the revised cuspidality criterion which are included here as Appendeix A. I have fixed the (earlier) proof of Theorem 2.0.4 by incorporating the revised cuspidality criterion. I thank Dinakar Ramakrishnan for bringing the problem to my attention and for a number of useful comments pertaining to the main result of this paper, in particular, for explaining the importance of Fourier coefficients rather than Hecke eigenvalues. I am indebted to Diprendra Prasaad for his crucial comments regarding the cuspidality criterion of the Asai transfer. In particular, thanks to both of them for providing Appendix A. I also thank Phil Kutzko and Freydoon Shahidi for useful discussions while writing this paper. It gives me great pleasure to dedicate this article to Freydoon Shahidi. I have been fortunate yo have studied mathematics under his tutelage and I am grateful for his support and guidance over the years. Finally, I am grateful to James Cogdell for his courtesy.Additional details
- Eprint ID
- 88615
- Resolver ID
- CaltechAUTHORS:20180806-142617876
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