Impact Factor: 0.8

Published since January 1, 1989

Forum Mathematicum

ISSN: 1435-5337

Edited by: Thomas Alazard, Chantal David, Manfred Droste, Siegfried Echterhoff, Jan Frahm, Maria Gordina, Philipp Habegger, Matthias Hieber, Clara Löh, Karin Melnick, Maksym Radziwill, Freydoon Shahidi, Christopher D. Sogge, Shigeharu Takayama

Managing Editor: Jan Hendrik Bruinier

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Forum Mathematicum (FORUM) is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.

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pure mathematics
applied mathematics
mathematical physics

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Highly Cited Paper*

On Barnes beta distributions, Selberg integral and Riemann xi
by: Ostrovsky, Dmitry
FORUM MATHEMATICUM Volume: 28 Issue: 1 Pages: 1-23 Published: JAN 2016

^{*A highly cited paper received enough citations to place it in the top 1% of the academic field of Mathematics based on a highly cited threshold for the field and publication year. (Data from Essential Science Indicators℠)}

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Volume 35 Issue 5

September 2023

Publicly Available September 1, 2023

Frontmatter

Page range: i-iv

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July 26, 2023

On the arithmetic of polynomial semidomains

Felix Gotti, Harold Polo

Page range: 1179-1197

Abstract

A subset S of an integral domain R is called a semidomain provided that the pairs ( S , + ) {(S,+)} and ( S , ⋅ ) {(S,\cdot\,)} are semigroups with identities. The study of factorizations in integral domains was initiated by Anderson, Anderson, and Zafrullah in 1990, and this area has been systematically investigated since then. In this paper, we study the divisibility and arithmetic of factorizations in the more general context of semidomains. We are specially concerned with the ascent of the most standard divisibility and factorization properties from a semidomain to its semidomain of (Laurent) polynomials. As in the case of integral domains, here we prove that the properties of satisfying the ascending chain condition on principal ideals, having bounded factorizations, and having finite factorizations ascend in the class of semidomains. We also consider the ascent of the property of being atomic and that of having unique factorization (none of them ascends in general). Throughout the paper, we provide several examples aiming to shed some light upon the arithmetic of factorizations of semidomains.

July 26, 2023

Extra-special Leibniz superalgebras

Gelareh Eghbali Kalhor, Behrouz Edalatzadeh, Ali Reza Salemkar

Page range: 1199-1209

Abstract

A two-step nilpotent Leibniz superalgebra L is called extra-special if the center and the derived subalgebra of L are equal and both are of dimension one. In this paper, the structure, the capability and the second homology of extra-special Leibniz superalgebras are determined.

March 29, 2023

Restricted iso-minimum condition

Asghar Daneshvar

Page range: 1211-1219

Abstract

A restricted artinian ring is a commutative ring with an identity in which every proper homomorphic image is artinian. Cohen proved that a commutative ring R is restricted artinian if and only if it is noetherian and every nonzero prime ideal of R is maximal. Facchini and Nazemian called a commutative ring isoartinian if every descending chain of ideals becomes stationary up to isomorphism. We show that every proper homomorphic image of a commutative noetherian ring R is isoartinian if and only if R has one of the following forms: (a) R is a noetherian domain of Krull dimension one which is not a principal ideal domain; (b) R ≅ D 1 × ⋯ × D k × A 1 × ⋯ × A l {R\cong D_{1}\times\cdots\times D_{k}\times A_{1}\times\cdots\times A_{l}} , where each D i {D_{i}} is a principal ideal domain and each A i {A_{i}} is an artinian local ring (either k or l may be zero); (c) R is a noetherian ring of Krull dimension one, simple unique minimal prime ideal 𝔭 {\mathfrak{p}} , and R / 𝔭 {R/\mathfrak{p}} is a principal ideal domain. As an application of our result, we describe commutative rings whose proper homomorphic images are principal ideal rings. Some relevant examples are provided.

May 3, 2023

On the spectral large sieve inequality for symmetric-squares

Matthew P. Young

Page range: 1221-1236

Abstract

We improve on the spectral large sieve inequality for symmetric-squares. We also prove a lower bound showing that the most optimistic upper bound is not true for this family.

May 3, 2023

Simple 𝔰𝔩(V)-modules which are free over an abelian subalgebra

Jonathan Nilsson

Page range: 1237-1255

Abstract

Let 𝔭 {\mathfrak{p}} be a parabolic subalgebra of 𝔰 ⁢ 𝔩 ⁢ ( V ) {\mathfrak{sl}(V)} of maximal dimension and let 𝔫 ⊂ 𝔭 {\mathfrak{n}\subset\mathfrak{p}} be the corresponding nilradical. In this paper, we classify the set of 𝔰 ⁢ 𝔩 ⁢ ( V ) {\mathfrak{sl}(V)} -modules whose restriction to U ⁢ ( 𝔫 ) {U(\mathfrak{n})} is free of rank 1. It turns out that isomorphism classes of such modules are parametrized by polynomials in dim ⁡ V - 1 {\dim V-1} variables. We determine the submodule structure for these modules and we show that they generically are simple.

June 27, 2023

Epsilon-strongly graded rings: Azumaya algebras and partial crossed products

Dirceu Bagio, Luis Martínez, Héctor Pinedo

Page range: 1257-1277

Abstract

Let G be a group, let A = ⊕ g ∈ G A g {A=\bigoplus_{g\in G}A_{g}} be an epsilon-strongly graded ring over G , let R := A 1 {R:=A_{1}} be the homogeneous component associated with the identity of G , and let 𝙿𝚒𝚌𝚂 ⁢ ( R ) {\mathtt{PicS}(R)} be the Picard semigroup of R . In the first part of this paper, we prove that the isomorphism class [ A g ] {[A_{g}]} is an element of 𝙿𝚒𝚌𝚂 ⁢ ( R ) {\mathtt{PicS}(R)} for all g ∈ G {g\in G} . Moreover, the association g ↦ [ A g ] {g\mapsto[A_{g}]} determines a partial representation of G on 𝙿𝚒𝚌𝚂 ⁢ ( R ) {\mathtt{PicS}(R)} which induces a partial action γ of G on the center Z ⁢ ( R ) {Z(R)} of R . Sufficient conditions for A to be an Azumaya R γ {R^{\gamma}} -algebra are presented if R is commutative. In the second part, we study when B is a partial crossed product in the following cases: B = M n ⁡ ( A ) {B=\operatorname{M}_{n}(A)} is the ring of matrices with entries in A , or B = END A ( M ) = ⊕ l ∈ G Mor A ( M , M ) l {B=\operatorname{END}_{A}(M)=\bigoplus_{l\in G}\operatorname{Mor}_{A}(M,M)_{l}} is the direct sum of graded endomorphisms of graded left A -modules M with degree l , or B = END A ⁡ ( M ) {B=\operatorname{END}_{A}(M)} where M = A ⊗ R N {M=A\otimes_{R}N} is the induced module of a left R -module N . Assuming that R is semiperfect, we prove that there exists a subring of A which is an epsilon-strongly graded ring over a subgroup of G and it is graded equivalent to a partial crossed product.

June 1, 2023

Non-weight modules over N = 1 Lie superalgebras of Block type

Qiang Xie, Jiancai Sun

Page range: 1279-1300

Abstract

In this paper, a class of non-weight modules over N = 1 {N=1} Lie superalgebras of Block type (without center) is studied. These modules over Ramond algebras of Block type are free of rank 1 when restricted to the universal enveloping algebra of the Cartan subalgebra, while such modules are free of rank 2 over the Neveu–Schwarz algebras of Block type. We present the classification of these modules. Furthermore, the simplicity of these modules is determined.

March 3, 2023

Simpler foundations for the hyperbolic plane

John Bamberg, Tim Penttila

Page range: 1301-1325

Abstract

H. L. Skala (1992) gave the first elegant first-order axiom system for hyperbolic geometry by replacing Menger’s axiom involving projectivities with the theorems of Pappus and Desargues for the hyperbolic plane. In so doing, Skala showed that hyperbolic geometry is incidence geometry. We improve upon Skala’s formulation by doing away with Pappus and Desargues altogether, by substituting for them two simpler axioms.

June 27, 2023

Characterizations of the mixed radial-angular central Campanato space via the commutators of Hardy type

Ronghui Liu, Shuangping Tao, Huoxiong Wu

Page range: 1327-1346

Abstract

In this paper, we introduce the mixed radial-angular central Campanato space ℭ ⁢ L rad p 2 , λ ⁢ L ang p 1 ⁢ ( ℝ n ) {{\mathfrak{C}L^{p_{2},\lambda}_{\mathrm{rad}}L^{p_{1}}_{\mathrm{ang}}(\mathbb% {R}^{n})}} and the mixed radial-angular central Morrey space 𝔐 ⁢ L rad p 2 , λ ⁢ L ang p 1 ⁢ ( ℝ n ) {{\mathfrak{M}L^{p_{2},\lambda}_{\mathrm{rad}}L^{p_{1}}_{\mathrm{ang}}(\mathbb% {R}^{n})}} , respectively. Characterizations of the mixed radial-angular central Campanato space are established via the boundedness of the commutators of Hardy type on the mixed radial-angular central Morrey space. Moreover, some characterizations of the mixed radial-angular λ-central bounded mean oscillation space CMO ⁡ L rad p 2 , λ ⁢ L ang p 1 ⁢ ( ℝ n ) {{\operatorname{CMO}L^{p_{2},\lambda}_{\mathrm{rad}}L^{p_{1}}_{\mathrm{ang}}(% \mathbb{R}^{n})}} are also obtained.

July 26, 2023

The fourth moment of Dirichlet L-functions along the critical line

Xiaosheng Wu

Page range: 1347-1371

Abstract

For a positive integer q ≢ 2 ⁢ ( mod ⁢ 4 ) {q\not\equiv 2~{}(\mathrm{mod}~{}4)} , this work considers the fourth moment of Dirichlet L -functions averaged over both t ∈ [ 0 , T ] {t\in[0,T]} and primitive characters modulo q . An asymptotic formula with a power saving from both the q -aspect and the t -aspect in the error term is obtained.

July 26, 2023

Diagonal restriction of Eisenstein series and Kudla–Millson theta lift

Romain Branchereau

Page range: 1373-1418

Abstract

We consider the Kudla–Millson theta series associated to a quadratic space of signature ( N , N ) {(N,N)} . By combining a “see-saw” argument with the Siegel–Weil formula, we show that its (regularized) integral along a torus attached to a totally real field of degree N is the diagonal restriction of an Eisenstein series. It allows us to express the Fourier coefficients of the diagonal restriction as intersection numbers, which generalizes a result of Darmon, Pozzi and Vonk to totally real fields.

June 1, 2023

Gibbons’ conjecture for quasilinear elliptic equations involving a gradient term

Phuong Le

Page range: 1419-1434

Abstract

We prove Gibbons’ conjecture for the quasilinear elliptic equation - Δ p ⁢ u + a ⁢ ( u ) ⁢ | ∇ ⁡ u | q = f ⁢ ( u ) in ⁢ ℝ N , -\Delta_{p}u+a(u)|\nabla u|^{q}=f(u)\quad\text{in }\mathbb{R}^{N}, where N ≥ 2 {N\geq 2} , 2 ⁢ N + 2 N + 2 < p < 2 {\frac{2N+2}{N+2}<p<2} , q ≥ 1 {q\geq 1} and a and f are Lipschitz continuous functions which satisfy some relevant conditions. This conjecture states that every weak solution u ∈ C 1 ⁢ ( ℝ N ) {u\in C^{1}(\mathbb{R}^{N})} of the equation with | u | ≤ 1 {|u|\leq 1} and lim x N → ± ∞ ⁡ u ⁢ ( x ′ , x N ) = ± 1 {\lim_{x_{N}\to\pm\infty}u(x^{\prime},x_{N})=\pm 1} , uniformly in x ′ ∈ ℝ N - 1 {x^{\prime}\in\mathbb{R}^{N-1}} , must depend only on x N {x_{N}} and ∂ ⁡ u ∂ ⁡ x N > 0 {\frac{\partial u}{\partial x_{N}}>0} in ℝ N {\mathbb{R}^{N}} . In particular, our result holds for a being non-decreasing on [ - 1 , - 1 + δ ] {[-1,-1+\delta]} and on [ 1 - δ , 1 ] {[1-\delta,1]} and f ⁢ ( u ) = | u | r ⁢ u ⁢ | 1 - u 2 | s ⁢ ( 1 - u 2 ) {f(u)=|u|^{r}u|1-u^{2}|^{s}(1-u^{2})} , where r , s , δ ≥ 0 {r,s,\delta\geq 0} . The main tool we use is an adaptation of the sliding method to the corresponding quasilinear elliptic operator.

July 1, 2023

Jantzen filtration of Weyl modules for general linear supergroups

Yi-Yang Li, Bin Shu

Page range: 1435-1468

Abstract

Let G = GL ⁡ ( m | n ) {G=\operatorname{GL}(m|n)} be a general linear supergroup over an algebraically closed field 𝐤 {\mathbf{k}} of odd characteristic p . In this paper, we construct Jantzen filtration of Weyl modules V ⁢ ( λ ) {V(\lambda)} for G when λ is a typical weight in the sense of Kac’s definition, and consequently obtain a sum formula for their characters. By Steinberg’s tensor product theorem, it is enough for us to study typical weights with aim to formulate irreducible characters. As an application, it turns out that an irreducible G -module L ⁢ ( λ ) {L(\lambda)} can be realized as a Kac module if and only if λ is p -typical.

Publicly Available June 1, 2023

Integral formulas for a class of curvature PDE’s and applications to isoperimetric inequalities and to symmetry problems

Vittorio Martino, Annamaria Montanari

Page range: 1469-1470

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Ahead of Print / Just Accepted

Ahead of Print / Just Accepted

Volume 35 (2023)

Volume 34 (2022)

Volume 33 (2021)

Volume 32 (2020)

Volume 31 (2019)

Volume 30 (2018)

Volume 29 (2017)

Volume 28 (2016)

Volume 27 (2015)

Volume 26 (2014)

Volume 25 (2013)

Volume 24 (2012)

Volume 23 (2011)

Volume 22 (2010)

Volume 21 (2009)

Volume 20 (2008)

Volume 19 (2007)

Volume 18 (2006)

Volume 17 (2005)

Volume 16 (2004)

Volume 15 (2003)

Volume 14 (2002)

Volume 13 (2001)

Volume 12 (2000)

Volume 11 (1999)

Volume 10 (1998)

Journal Impact Factor	0.8	2022, Journal Citation Reports (Clarivate, 2023)
5-year Journal Impact Factor	0.8	2022, Journal Citation Reports (Clarivate, 2023)
Journal Citation Indicator	0.64	2022, Journal Citation Reports (Clarivate, 2023)
CiteScore	1.6	2022, Scopus (Elsevier B.V., 2023)
SCImago Journal Rank	0.786	2022, SJR (Scimago Lab, 2023; Data Source: Scopus)
Source Normalized Impact per Paper	0.989	2022, CWTS Journal Indicators (CWTS B.V., 2023; Data Source: Scopus)
Mathematical Citation Quotient	0.86

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Editorial

Managing Editor

Jan H. Bruinier
Department of Mathematics
Technische Universität Darmstadt
bruinier@mathematik.tu-darmstadt.de
Primary research areas: Number theory, automorphic forms, algebraic geometry.

Editors

Thomas Alazard
CNRS and École Normale Supérieure Paris-Saclay
thomas.alazard@ens-paris-saclay.fr
Main research areas : partial differential equations,microlocal analysis, mathematical problems in fluid dynamics

Chantal David
Department of Mathematics and Statistics
Concordia University
chantal.david@concordia.ca
Primary research areas:　Analytic number theory, L-functions, arithmetic statistics.

Manfred Droste
Institut für Informatik
Universität Leipzig
droste@informatik.uni-leipzig.de
Primary research areas: Group theory, logic, ordered structures, automata theory.

Siegfried Echterhoff
Mathematisches Institut
Universität Münster
echters@uni-muenster.de
Primary research areas: Functional analysis, operator algebras, K-theory

Jan Frahm
Department of Mathematics
Aarhus University
frahm@math.au.dk
Primary research areas: Lie theory, harmonic analysis, homogeneous spaces

Maria Gordina
Department of Mathematics
University of Connecticut
maria.gordina@uconn.edu
Primary research areas: Probability theory and stochastic processes, global analysis, analysis on manifolds

Philipp Habegger
Universität Basel
Departement Mathematik und Informatik
Basel, Schweiz
philipp.habegger@unibas.ch
Research areas: Number Theory, Diophantine Geometry

Matthias Hieber
Department of Mathematics
TU Darmstadt, Germany
hieber@mathematik.tu-darmstadt.de
Primary research areas are: partial differential equations, fluid dynamics

Clara Löh
Faculty of Mathematics
University of Regensburg
clara.loeh@mathematik.uni-regensburg.de
Primary research areas are: Geometric Topology, Geometric Group Theory, Measured Group Theory

Karin Melnick
Department of Mathematics
University of Luxembourg
karin.melnick@uni.lu

Primary research areas: differential geometry, transformation groups

Maksym Radziwill
Department of Mathematics
Caltech, Pasadena
maksym.radziwill@gmail.com
Primary research areas: Analytic Number Theory

Freydoon Shahidi
Department of Mathematics
Purdue University
shahidi@math.purdue.edu
Primary research areas: Automorphic forms, group representations, number theory and arithmetic geometry.

Christopher D. Sogge
Department of Mathematics
Johns Hopkins University
sogge@jhu.edu
Primary research areas: Fourier analysis, partial differential equations.

Shigeharu Takayama
Department of Mathematics
University of Tokyo
taka@ms.u-tokyo.ac.jp
Primary research areas: complex geometry, Kähler geometry and algebraic geometry

Editorial Office at De Gruyter

Masha Dorogova
Journal Coordinator Forum Mathematicum
masha.dorogova@degruyter.com

(Deutsch)

Online ISSN: 1435-5337
Print ISSN: 0933-7741
Type: Journal
Language: English
Publisher: De Gruyter
First published: January 1, 1989
Publication Frequency: 6 Issues per Year
Audience: researchers in the field of mathematics