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Results tagged with hecke-operators
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user 116092
23
votes
2
answers
2k
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What is the matter with Hecke operators?
This question is inspired by some others on MathOverflow. Hecke operators are standardly defined by double cosets acting on automorphic forms, in an explicit way.
However, what bother me is that Hec …
- 5,424
3
votes
0
answers
290
views
Ramanujan conjecture in terms of representations
Given an automorphic representation, I would like to bound $\alpha_1^\nu(p) + \alpha_2^\nu(p)$ where the $\alpha_i$ are the Satake parameters of an automorphic form $f$ of, say, $GL_2$. So that $\alph …
- 609
6
votes
0
answers
246
views
Local L-factors for automorphic representations
For Hecke L-functions associated to a holomorphic cusp form $f$ of level $N$, the local factors can be decomposed into
$$L_p(s, f) = (1-\lambda_f(p)p^{-s} + \chi_N(p)p^{-2s})^{-1}$$
where $\chi_N$ is …
- 609