Suppose X is a compact Kähler manifold of dimension n and E is a holomorphic vector bundle. For every p ≤ dim C X we have a sheaf Ω p (E) whose sections are holomorphic (p, 0)-forms with coefficients in E. We set and we define the holomorphic Euler characteristics χ p (X, E) := q≥0 (−1) q h p,q (X, E). It is convenient to introduce the generating function of these numbers χ y (X, E) := p≥0 y p ...

We study the finite groups G with a faithful irreducible character whose square is a linear combination of algebraically conjugate irreducible characters of G. In conclusion, we offer another proof of one theorem of Isaacs-Zisser. There are a few papers treating the finite groups possessing an irreducible character whose powers are linear combinations of appropriate irreducible characters, for ...

Let χ be a finite Borel measure on [0, 1]. Consider the L-spectrum of χ: τχ(q) = lim infn→∞−n logb P Q∈Gn, χ(Q) 6=0 χ(Q) , where Gn is the set of b-adic cubes of generation n. Let qτ = inf{q : τχ(q) = 0} and Hτ = τ ′ χ(q − τ ). When χ is a mono-dimensional continuous measure of information dimension D, (qτ , Hτ ) = (1, D). When χ is purely discontinuous, its information dimension is D = 0, but ...

where the parameter f fπ 92.4 MeV is known from the decay process of charged pions. In contrast to the successful application of the chiral Lagrangian in the flavor SU(2) sector, its application to the strange sector of QCD is flawed by a number of subtleties if the machinery of chiral perturbation theory is applied. The leading interaction term fails miserably in describing the s-wave scatteri...

Every Hecke character of K satisfying (1.1) and (1.2) is actually a quadratic twist of a canonical Hecke character (see Section 2 for a precise description of these characters and which fields have them). Let L(s, χ) denote the Hecke L-function of χ, and Λ(s, χ) its completion; Λ(s, χ) satisfies the functional equation Λ(s, χ) = W (χ)Λ(2 − s, χ), where W (χ) = ±1 is the root number. If χ is a c...