Eisenstein series for rank one unitary groups and some cohomological applications

Periods of Eisenstein Series and Some Applications

Bringmann, Guerzhoy, Ono, and the author recently developed an Eichler-Shimura theory for weakly holomorphic modular forms by studying associated period polynomials. Here we include the Eisenstein series in this theory. Classically, the periods of a weight k (k ≥ 4 will always denote an even integer) cusp form f = ∑ l≥1 af (l)q l (q := e with τ = x+ iy ∈ C with y > 0) on Γ := SL2(Z) are given by

Compact Periods of Eisenstein Series of Orthogonal Groups of Rank One

We determine the period of a spherical Eisenstein series Eφ of an orthogonal group G = O(n + 3) of rank one, along the anisotropic subgroup H = O(n + 2). We unwind the global period (Eφ)H = Z Hk\HA Eφ into an Euler product and evaluate the local factors at good non-archimedean places. Introduction Let G = O(n+ 3) have rank one, H = O(n + 2) be an anisotropic subgroup of G, and k be a number fie...

Compact periods of Eisenstein series of orthogonal groups of rank one at even primes

Fix a number field k with its adele ring A. Let G = O(n+3) be an orthogonal group of k-rank 1 and H = O(n + 2) a k-anisotropic subgroup. We have previously described how to factor the global period

Eisenstein Series and Their Applications

Meromorphic continuation of higher-rank Eisenstein series

Expanded version of a talk given in Tel Aviv, Israel, 22 March 2001. To trivialize the proof of meromorphic continuation of Eisenstein series, we want to use only standard facts, together with Bernstein’s formulation of a continuation principle. In particular, one should prove meromorphic continuation as a vector-valued function, from which one infers that the continuation is of moderate growth...