Generating functions on covering groups
Keyword(s):
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 $\text{GL}_{r}^{(n)}(\mathbf{A})$.
2021 ◽
Vol 13
(2)
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pp. 413-426
2011 ◽
Vol 21
(07)
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pp. 1217-1235
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2014 ◽
Vol 23
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pp. 1057-1086
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1990 ◽
Vol 431
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pp. 403-417
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