1 results
Generating functions on covering groups
- Part of
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- Journal:
- Compositio Mathematica / Volume 154 / Issue 4 / April 2018
- Published online by Cambridge University Press:
- 20 February 2018, pp. 671-684
- Print publication:
- April 2018
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- Article
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In this paper we prove a conjecture relating the Whittaker function of a certain generating function with the Whittaker function of the theta representation
$\unicode[STIX]{x1D6E9}_{n}^{(n)}$. This enables us to establish that a certain global integral is factorizable and hence deduce the meromorphic continuation of the standard partial 
$L$ function 
$L^{S}(s,\unicode[STIX]{x1D70B}^{(n)})$. In fact we prove that this partial 
$L$ function has at most a simple pole at 
$s=1$. Here, 
$\unicode[STIX]{x1D70B}^{(n)}$ is a genuine irreducible cuspidal representation of the group 
$\text{GL}_{r}^{(n)}(\mathbf{A})$.
