Eisenstein series on orthogonal groups ${\rm O}(1,m+1)$ and ${\rm O}(2,m+2)$

Bank ownership, rm value and rm capital structure in Europe*

We investigate the role of banks in the ownership structure of non-…nancial …rms. Distinguishing between banks and other institutional investors as shareholders, we examine the relationship between …nancial institution ownership and the performance of the …rms in which they hold equity. We control explicitly for the capital structure decision of the …rms and the ownership decision of …nancial i...

Topological superconductor in quasi-one-dimensional ${\rm Tl}_{2-x}{\rm Mo}_6{\rm Se}_6$

Identifying an Honest ${\rm EXP}^{\rm NP}$ Oracle Among Many

We provide a general framework to remove short advice by formulating the following computational task for a function f : given two oracles at least one of which is honest (i.e. correctly computes f on all inputs) as well as an input, the task is to compute f on the input with the help of the oracles by a probabilistic polynomial-time machine, which we shall call a selector. We characterize the ...

Transition: Eisenstein series on adele groups

[1] Despite contrary assertions in the literature, rewriting Eisenstein series, as opposed to more general automorphic forms, on adele groups does not use Strong Approximation. Strong Approximation does make precise the relation between general automorphic forms on adele groups and automorphic forms on SL2 and even on SLn, but rewriting these Eisenstein series does not need this comparison. Ind...

Computations of Eisenstein series on Fuchsian groups

We present numerical investigations of the value distribution and distribution of Fourier coefficients of the Eisenstein series E(z; s) on arithmetic and non-arithmetic Fuchsian groups. Our numerics indicate a Gaussian limit value distribution for a real-valued rotation of E(z; s) as Re s = 1/2, Im s → ∞ and also, on non-arithmetic groups, a complex Gaussian limit distribution for E(z; s) when ...