Value-distribution of twisted automorphic <Emphasis Type="Italic">L</Emphasis>-functions

In this paper, we prove a limit theorem for twisted with character automorphic L-functions with an increasing modulus of the character.     

Multiplicity Free Expansions of Schur <Emphasis Type="Italic">P</Emphasis>-Functions

After deriving inequalities on coefficients arising in the expansion of a Schur P-function in terms of Schur functions we give criteria for when such expansions are multiplicity free. From here we study the multiplicity of an irreducible spin character of the twisted symmetric group in the product of a basic spin character with an irreducible character of the symmetric group, and determine when it is multiplicity free. Received February 28, 2005     

Value-distribution of twisted automorphic <Emphasis Type="Italic">L</Emphasis>-functions. II

In this paper, we prove a limit theorem for the argument of twisted with character automorphic L-functions with an increasing modulus of the character.     

A character theoretic criterion for a <Emphasis Type="Italic">p</Emphasis>-closed group

In this paper, we obtain a character theoretic criterion for a group to be p-closed.     

Nonexistence of <Emphasis Type="Italic">CW</Emphasis>(110, 100)

Using character theoretic methods, we settle the existence status of a circulant weighing matrix of order 110 with weight 100. This fills a missing entry in recent tables, thereby answering the existence of previously open CW (110,100) with answer “NO”.     

Universal Karoubi characteristic classes of nuclear <Emphasis Type="Italic">C</Emphasis>*-algebras

The main result of this paper is the evaluation of kernels for the Chern character and the universal Karoubi classes of nuclear C*-algebras. It is shown that the kernel of the Chern character coincides with the subgroup of infinitely small elements of the K ₀-group and the kernel of the universal Karoubi classes coincides with the subgroup of approximately scalar elements of the K ₀-group. Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 8, pp. 133–169, 2007.     

Unitarization of Schur representations of a partially ordered set associated with <Emphasis Type="Italic">Ẽ</Emphasis>7

We prove that every Schur representation of a partially ordered set associated with graph Ẽ ₇ can be unitarized with some character.     

On critical values of twisted Artin <Emphasis Type="Italic">L</Emphasis>-functions

We give a simple proof that critical values of any Artin L-function attached to a representation ? with character χ _? are stable under twisting by a totally even character χ, up to the dim ?-th power of the Gauss sum related to χ and an element in the field generated by the values of χ _? and χ over ?. This extends a result of Coates and Lichtenbaum as well as the previous work of Ward.     

Characterizations of some rings with <Emphasis Type="Italic">C</Emphasis>-projective, <Emphasis Type="Italic">C</Emphasis>-(FP)-injective and <Emphasis Type="Italic">C</Emphasis>-flat modules

Let R be a commutative ring and C a semidualizing R-module. We investigate the relations between C-flat modules and C-FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.     

Localisation de faisceaux caractères

We obtain a formula for the values of the characteristic function of a character sheaf, in terms of the representation theory of certain finite groups related to the Weyl group. This formula, a generalization of previous results due to Mœglin and Waldspurger, depends on knowledge of certain reductive subgroups that admit cuspidal character sheaves. For quasi-simple groups, we make the formula truly explicit by determining all such subgroups upto conjugation.     

Pseudo-coefficients des séries <Emphasis Type="Italic">κ</Emphasis>-discrètes de GL(<Emphasis Type="Italic">n,F</Emphasis>)

Let F be a non-Archimedean locally compact field, n be an integer ≥ 2, κ be a character of F ^× of finite order dividing n, and G be the group GL(n, F). We prove that if π is an irreducible κ-discrete series of G, then there exist some pseudo-coefficients for the twisted character trace(π ∘ A) where A denotes a non-zero intertwining operator between π ⊗ (κ ∘ det) and π.     

Finite groups with a <Emphasis Type="Italic">D</Emphasis>-block of cardinality 3

The results of this paper are connected with one of the main problems of the representation theory, the problem of dependence between the character table of a finite group and its abstract structure. Finite groups that have a D-block of cardinality 3 for some normal subset D are investigated. Some properties of classical p-blocks (where p is a prime number) consisting of three irreducible characters are also obtained.     

A geometry for groups of <Emphasis Type="Italic">J</Emphasis><Subscript>3</Subscript>-type

The proof of the existence and of the uniqueness of groups of J₃-type by G. Higman and J. McKay is based on the fact that a group of J₃-type is a faithful completion of an amalgam of J₃-type, see [11]. In this paper here, we provide a direct reference for that fact. The proofs in this paper are elementary and we do not use any character theory. Received: 1 December 2005     

On the 2<Emphasis Type="Italic">k</Emphasis>-th Power Mean of Inversion of <Emphasis Type="Italic">L</Emphasis>-functions with the Weight of the Gauss Sum

Abstract The main purpose of this paper is to use the estimate for character sums and the method of trigonometric sums to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of the Gauss sums, and give a sharper asymptotic formula. This work is supported by the Doctorate Foundation of Xi’an Jiaotong University     

Dualité dans l’espace des caractères virtuels tempérés d’un groupe réductif <Emphasis Type="Italic">p</Emphasis>-adique

Résumé We define an involution on the set of tempered virtual characters of a connected reductive p-adic group. This involution commutes with character of parabolic induction and with truncation. It also preserves the irreducible characters up to sign and the elliptic inner product.     

The First Power Mean of the Inversion of L-Functions Weighted by Quadratic Gauss Sums

The main purpose of this paper is to use estimates for character sums and analytic methods to study the first power mean of the inversion of Dirichlet L-functions with the weight of general quadratic Gauss sums, and three asymptotic formulae are obtained.     

On a Projection from One Co – Invariant Subspace onto Another in Character – Automorphic Hardy Space on a Multiply Connected Domain

In a case of a theory in a unit disk the solution of a problem on the invertibility of an orthogonal projection from one co–invariant subspace of the shift operator onto another turned out to be essential for the solution of the problem on the Riesz basis property of the reproducing kernels and in particular for the solution of the problem on the basis of exponentials in L₂ space on a segment. In the present paper we are dealing with the similar problems in harmonic analysis on a finitely connected domain. Namely we obtain necessary and sufficient conditions for the invertibility of an orthogonal projection from one co – invariant subspace of character – automorphic Hardy space in the domain onto another. The given condition has a form of a Muckenhoupt condition for a certain weight on the boundary of the domain, but essentially depends on a character. Namely, for two fixed character – automorphic inner functions, which define the co – invariant subspaces, the projection may be invertible for one character and not invertible for another.