Adrian, Moshe, Liu, Baiying, Stevens, Shaun and Tam, Geo Kam-Fai
(2018)
*On the sharpness of the bound for the Local Converse Theorem of p-adic GLprime.*
Proceedings of the American Mathematical Society, Series B, 5.
pp. 6-17.
ISSN 2330-1511

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## Abstract

We introduce a novel ultrametric on the set of equivalence classes of cuspidal irreducible representations of a general linear group GL(N) over a nonarchimedean local field, based on distinguishability by twisted gamma factors. In the case that N is prime and the residual characteristic is greater than or equal to N/2, we prove that, for any natural number i at most N/2, there are pairs of cuspidal irreducible representations whose logarithmic distance in this ultrametric is precisely i. This implies that, under the same conditions on N, the bound N/2 in the Local Converse Theorem for GL(N) is sharp.

Item Type: | Article |
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Faculty \ School: | Faculty of Science > School of Mathematics (former - to 2024) |

UEA Research Groups: | Faculty of Science > Research Groups > Algebra and Combinatorics Faculty of Science > Research Groups > Number Theory (former - to 2017) |

Depositing User: | Pure Connector |

Date Deposited: | 02 Nov 2017 10:43 |

Last Modified: | 12 Sep 2024 00:09 |

URI: | https://ueaeprints.uea.ac.uk/id/eprint/65335 |

DOI: | 10.1090/bproc/32 |

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