Naslov
Eisenstein series for rank one unitary groups and some cohomological applications

Autori
Grbac, Neven ; Schwermer, Joachim

Izvornik
Advances in mathematics (0001-8708) 376 (2021); 107438, 48

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Eisenstein cohomology ; Automorphic representations ; Eisenstein series ; Arithmetic groups ; Unitary groups ; Automorphic L-functions

Sažetak
Let U/Q be a unitary group of Q-rank one so that the group of real points U(R) congruent to U(n, 1). The group U is only quasi split over Q if and only if n = 1, 2. The cohomology of a congruence subgroup of U is closely related to the theory of automorphic forms. This relation is best captured in the socalled automorphic cohomology spaces H* (U, C), a natural module under the action of the group U(A(f)). This paper gives a structural account of the U(A(f))-module structure of that part of the cohomology which is generated by residues or derivatives of Eisenstein series. In particular, we determine a set of arithmetic conditions, mainly given in terms of partial automorphic L-functions, subject to which residues of Eisenstein series may give rise to non- vanishing cohomology classes. The main task is, although the usual method due to Langlands-Shahidi is not applicable, to analyze the analytic behavior of suitable Eisenstein series and to determine the location of their possible poles.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Računarstvo

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