In this paper we show a local Jacquet-Langlands correspondence for all unitary irreducible representations. We prove the global Jacquet-Langlands correspondence in characteristic zero. As consequences we obtain the multiplicity one and strong multiplicity one theorems for inner forms of GL(n) as well as a classification of the residual spectrum and automorphic representations in analogy with results proved by Moeglin-Waldspurger and Jacquet-Shalika for GL(n).
Abstract. In this paper we decompose the residual spectrum supported in the minimal parabolic subgroup of an inner form of the split group SO 8 . The approach is the Langlands spectral theory. However, since the group is non-quasi-split, it is out of the scope of the Langlands-Shahidi method and the new technique for the normalization of standard intertwining operators is developed. The decomposition shows interesting parts of the residual spectrum not appearing in the case of quasi-split groups.
The cohomology of an arithmetically defined subgroup of the symplectic Q-group Spn is closely related to the theory of automorphic forms. This paper gives a structural account of that part of the cohomology which is generated by residues or derivatives of Eisenstein series of relative rank one. In particular we determine a set of conditions subject to which residues of Eisenstein series may give rise to non-vanishing cohomology classes. A non-vanishing condition on the value at s = 1/2 of certain automorphic L-functions which naturally appear in the constant terms of the Eisenstein series plays a major role.
Electrophonic meteor sounds, heard simultaneously with the meteor appearance, are a longstanding problem due to their nonintuitive nature. Previous investigations have been undermined by lack of instrumental recordings. Here we present the first instrumental detection of electrophonic sounds obtained during the observation of 1998 Leonids from Mongolia. Two Leonid fireballs of brightness −6.5m and −12m produced short, low‐frequency sounds, which were simultaneously recorded by microphones in a special setup and heard by different observers. Simultaneous measurements of electromagnetic ELF/VLF radiation above 500 Hz did not reveal any signal correlated to the electrophonic event. The lack of signal was explained by the low frequency of electrophones. We show that physical characteristics of Leonid electrophones cannot be completely explained by existing theories and that further theoretical refinement and observational work is needed. Finally, we tentatively suggest the possibility of stronger than expected coupling of fireballs with atmospheric charge dynamics and ionosphere.
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