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Towards the Jacquet conjecture on the Local Converse Problem for p -adic GL n

Dihua Jiang, Chufeng Nien, Shaun Stevens (2015)

Journal of the European Mathematical Society

The Local Converse Problem is to determine how the family of the local gamma factors γ ( s , π × τ , ψ ) characterizes the isomorphism class of an irreducible admissible generic representation π of GL n ( F ) , with F a non-archimedean local field, where τ runs through all irreducible supercuspidal representations of GL r ( F ) and r runs through positive integers. The Jacquet conjecture asserts that it is enough to take r = 1 , 2 , ... , n 2 . Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet conjecture,...

Trace formulae and applications to class numbers

Nicole Raulf (2014)

Open Mathematics

In this paper we compute the trace formula for Hecke operators acting on automorphic forms on the hyperbolic 3-space for the group PSL2( 𝒪 K ) with 𝒪 K being the ring of integers of an imaginary quadratic number field K of class number H K > 1. Furthermore, as a corollary we obtain an asymptotic result for class numbers of binary quadratic forms.

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