Malicki, Maciej
Published in
Forum Mathematicum

The paper is devoted to a study of isometry groups of Polish ultrametric spaces. We explicitly describe isometry groups of spaces that are non-locally rigid and satisfy the property that distances between orbits under the action of the isometry group are realized by points. The type of group construction appearing here is a variant of the generaliz...

Bose, Debashish Madan, Shobha
Published in
Forum Mathematicum

Bose, Anil Kumar, Krishnan and Madan (2010) showed that “Tiling implies Spectral” holds for a union of three intervals and the reverse implication was studied under certain restrictive hypotheses on the associated spectrum. In this paper, we reinvestigate the “Spectral implies Tiling” part of Fuglede's conjecture for the three interval case. We fir...

Grbac, Neven Schwermer, Joachim
Published in
Forum Mathematicum

The automorphic cohomology of a reductive ℚ-group G, defined in terms of the automorphic spectrum of G, captures essential analytic aspects of the arithmetic subgroups of G and their cohomology. The subspace spanned by all possible residues and principal values of derivatives of Eisenstein series, attached to cuspidal automorphic forms π on the Lev...

Catino, Francesco Lee, Gregory T. Spinelli, Ernesto
Published in
Forum Mathematicum

Let F be a field of characteristic p ≠ 2 and G a group without 2-elements having an involution *. Write (FG) + $(FG)^+$ for the set of elements in the group ring FG that are symmetric with respect to the induced involution. In the present note, we show that if G is finite and (FG) + $(FG)^+$ is Lie metabelian, then G is nilpotent. Based on this res...

Languasco, Alessandro Zaccagnini, Alessandro
Published in
Forum Mathematicum

Let Λ be the von Mangoldt function and r G (n)=∑ m 1 +m 2 =n Λ(m 1 )Λ(m 2 )$ {r_G(n) = \sum _{m_1 + m_2 = n} \Lambda (m_1) \Lambda (m_2)} $ be the counting function for the Goldbach numbers. Let N ≥ 2 be an integer. We prove that ∑ n≤N r G (n)(1-n N) k Γ(k+1)=N 2 Γ(k+3)-2∑ ρ Γ(ρ) Γ(ρ+k+2)N ρ+1 +∑ ρ 1 ∑ ρ 2 Γ(ρ 1 )Γ(ρ 2 ) Γ(ρ 1 +ρ 2 +k+1)N ρ 1 +ρ 2 ...

Lück, Wolfgang Rosenthal, David
Published in
Forum Mathematicum

We investigate the algebraic K- and L-theory of the group ring RG, where G is a hyperbolic or virtually finitely generated abelian group and R is an associative ring with unit.

Delabarre, Ludovic
Published in
Forum Mathematicum

This work is an answer to a problem posed by N. Kurokawa and H. Ochiai concerning the natural boundary of meromorphy of a multivariate Euler product of Igusa type. More generally, we introduce and determine the maximal domain of meromorphy of a class of multivariate non-uniform Euler products.

Ballester-Bolinches, Adolfo Pin, Jean-Éric Soler-Escrivà, Xaro
Published in
Forum Mathematicum

We present an extension of Eilenberg's variety theorem, a well-known result connecting algebra to formal languages. We prove that there is a bijective correspondence between formations of finite monoids and certain classes of languages, the formations of languages. Our result permits to treat classes of finite monoids which are not necessarily clos...

Ahlgren, Scott Kim, Byungchan
Published in
Forum Mathematicum

We construct and study several infinite grids of mock modular forms. The “rows” of each grid encode an infinite family of forms, while the “columns” encode a second infinite family. Each of these grids contains a generating function of interest as its first entry (for example, the “smallest parts” function of Andrews, or a mock theta function of Ra...

Matthes, Roland Mizuno, Yoshinori
Published in
Forum Mathematicum

We study some arithmetics of Hermitian modular forms of degree two by applying the spectral theory on 3-dimensional hyperbolic space. This paper presents three main results: (1) a 3-dimensional analogue of Katok–Sarnak's correspondence, (2) an analytic proof of a Hermitian analogue of the Saito–Kurokawa lift by means of a converse theorem, (3) an e...