This paper is a continuation of [HT]. Let L be an imaginary CM field and let Π be a regular algebraic (i.e., Π∞ has the same infinitesimal character as an algebraic representation of the restriction of scalars from L to Q of GLn) cuspidal automorphic representation of GLn(AL) which is conjugate self-dual (Π ◦ c ∼= Π∨) and square integrable at some finite place. In [HT] it is explained how to at...

in the crystal structure of the title polymeric compound, [c42h38n6o33sr5.2(h2o)]n, five independent metal atoms (sr1-sr5) have different coordination environments. the sr1 and sr5 atoms are nine coordinated and feature distorted tricapped trigonal-prismatic and capped square-antiprismatic geometries, respectively. the rest srii atoms have eight coordination numbers. these units are connected v...

In this work, the effect of regulated host and auxiliary ligand π-conjugation on the photophysical properties of a series of Ir(III) carbene complexes is examined by using the start-of-the-art theoretical methods. According to our results, all of the lowest-lying and strongest absorption peaks can be assigned as having a mixed ligand-to-ligand/metal-to-ligand charge transfer (LLCT/MLCT) charact...

For K/F a quadratic extension of p-adic fields, let σ be the conjugation relative to this extension, and ηK/F be the character of F ∗ with kernel norms of K. If π is a smooth irreducible representation of GL(n,K), and χ a character of F , the dimension of the space of linear forms on its space, which transform by χ under GL(n, F ) (with respect to the action [(L, g) 7→ L ◦ π(g)]) , is known to ...

High-valent transition-metal-substituted Keggin-type polyoxometalates (POMs) are active and robust oxidation catalyst. The important oxidized intermediates of these POM complexes are very difficult to be characterized by using the experimental method, and thus no detail information is available on such species. In the present paper, density functional theory (DFT) calculations have been carried...

Let π be a Hecke-Maass cusp form for SL(3,Z) and χ = χ1χ2 a Dirichlet character with χi primitive modulo Mi. Suppose that M1, M2 are primes such that max{(M |t|)1/3+2δ/3,M2/5|t|−9/20,M1/2+2δ|t|−3/4+2δ}(M |t|)ε < M1 < min{(M |t|)2/5, (M |t|)1/2−8δ}(M |t|)−ε for any ε > 0, where M = M1M2, |t| ≥ 1 and 0 < δ < 1/52. Then we have L ( 1 2 + it, π ⊗ χ ) ≪π,ε (M |t|).

Let π be a regular algebraic cuspidal automorphic representation of GL2 over an imaginary quadratic number field K, and let ` be a prime number. Assuming the central character of π is invariant under the non-trivial automorphism of K, it is shown that there is a continuous irreducible `-adic representation ρ of Gal(K/K) such that L(s, ρv) = L(s, πv) whenever v is a prime of K outside an explici...

Let π be a regular algebraic cuspidal automorphic representation of GL2 over an imaginary quadratic number field K, and let l be a prime number. Assuming the central character of π is invariant under the non-trivial automorphism of K, it is shown that there is a continuous irreducible l-adic representation ρ of Gal(K/K) such that L(s, ρv) = L(s, πv) whenever v is a prime of K outside an explici...

Let F be a finite extension of Qp and K a quadratic extension of F . If (Π, V ) is a representation of GL2(K), H a subgroup of GL2(K) and μ a character of the image subgroup det(H) of K∗, then Π is said to be μ-distinguished with respect to H if there exists a nonzero linear form l on V such that l(Π(g)v) = μ(det g)l(v) for g ∈ H and v ∈ V . We provide new proofs, using entirely local methods, ...