Editors: D. Bao (San Francisco, SFSU), S. Berhanu (Temple), D. Blecher
(Houston), B. G. Bodmann (Houston),
M. Gehrke (CNRS),
Y. Hattori (Matsue, Shimane), A. Haynes (Houston), W. B. Johnson (College Station), H. Koivusalo (Bristol),
T. H. Lê (Mississippi),
M. Marsh (Sacramento),
M. Ru (Houston), S. W. Semmes (Rice), D. Werner (FU Berlin).
Managing Editors: B. G. Bodmann and A. Haynes (Houston)
Houston Journal of Mathematics
Contents
Huaifu Liu, School of Mathematics, Statistics and Mechanics, Beijing University of
Technology, Beijing 100124, China (liuhf@bjut.edu.cn), Lei Huang, School
of Mathematics, Statistics and Mechanics, Beijing University of Technology,
Beijing 100124, China (hl421@emails.bjut.edu.cn), and Xiaohuan Mo, School of
Mathematics and Statistics, Henan Normal University, Xinxiang 453007, China;
School of Mathematical Sciences, Peking University, Beijing 100871, China
(moxh@pku.edu.cn).
On a class of Finsler spaces with constant flag curvature and cohomogeneity not
exceeding two, pp. 209–229.
ABSTRACT. In this paper, we study a class of projective flat Finsler spaces with
constant flag curvature and cohomogeneity not exceeding two. We find equations that
characterize these metrics generalizing results previously only known in the case of
spherically symmetric Finsler metrics. Moreover, we manufacture new 2-dimensional
family of projectively flat Finsler metrics of negative constant flag curvature. These
metrics contain Chern-Shen’s construction in Riemann-Finsler geometry, Nankai Tracts
in Mathematics, Vol 6 (World Scientific Publishing, Hackensack, NJ, 2005), X+192pp.
Nathan Grieve, Laboratory for Birational Geometry, Astronomy Mathematics Building
5F, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan (R.O.C.); School of Mathematics
and Statistics, Carleton University, 4302 Herzberg Laboratories, 1125 Colonel By Drive,
Ottawa, ON, K1S 5B6, Canada; Département de mathématiques, Université
du Québec à Montréal, Local PK-5151, 201 Avenue du Président-Kennedy,
Montréal, QC, H2X 3Y7, Canada; Department of Pure Mathematics, University
of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada
(nathan.m.grieve@gmail.com).
Effective calculation of local Weil functions via presentations of Cartier divisors, pp.
231–245.
ABSTRACT. We address the question of effectivity for calculation of local
Weil functions from the viewpoint of presentations of Cartier divisors. This
builds on the approach of Bombieri and Gubler as well as the perspective of our
earlier works. Among other features, our approach here gives rise to theoretical
effective algorithms for calculating local Weil functions on projective varieties.
Rafael López, Departamento de Geometría y Topología, Universidad de Granada,
18071 Granada, Spain (rcamino@ugr.es).
A note on helicoidal singular minimal surfaces, pp. 247–255.
ABSTRACT. Let α ∈ ℝ and let 
∈ ℝ3 be a unit vector. An α-singular minimal surface
Σ in Euclidean space is a surface whose mean curvature H satisfies H = α
, where
N is the unit normal vector of Σ. In this short note, we prove that if Σ is a
helicoidal α-singular minimal surface, then the twist axis of the helicoidal motion is
orthogonal to 
, the parameter α is α = −1 and Σ is a circular right cylinder.
Young Jin Suh, Department of Mathematics and RIRCM, Kyungpook National
University, Daegu 41566, Republic of Korea (yjsuh@knu.ac.kr).
Real hypersurfaces with pseudo-Ricci-Yamabe solitons in the complex hyperbolic
quadric, pp. 257–290.
ABSTRACT. First we introduce a new notion of pseudo-anti commuting for real
hypersurfaces in the noncompact complex hyperbolic quadric Qm∗ = SO2,mo∕SO2SOm
and give a complete classification of Hopf real hypersurfaces in the complex hyperbolic
quadric Qm∗ which admits a pseudo-Ricci-Yamabe soliton. It becomes a tube over a
complex hyperbolic space ℂHk in Q2k∗ or a horosphere of 𝔄-isotropic singular. Next as
an application we obtain a classification of gradient pseudo-Ricci-Yamabe solitons on
Hopf real hypersurfaces in Qm∗.
Jiaqi Liu, School of Mathematics and Statistics, Henan University, Kaifeng
475004, Henan, China (15535650053@163.com), and Wei Zhang, School of
Mathematics and Statistics, Henan University, Kaifeng 475004, Henan, China
(zhangweimath@126.com).
On a sum involving certain arithmetic functions on Piatetski-Shapiro, Beatty and
fractional sequences, pp. 291–307.
ABSTRACT. Let c,t,α,β ∈ ℝ be such that 1 < c < 2,0 < t ≤ 1,α > 1 is irrational and with bounded partial quotients, β ∈ [0,α). In this paper, we study asymptotic behaviour of the summations of the form
![∑ f([nc]) ∑ f([αn+ β]) ∑ f([x ])
-[nc]t- , -[αn+-β-]t- and -[nx]t--,
1≤n≤x 1≤n ≤x 1≤n≤x n](Vol51-23x.png)
where f is the Euler totient function ϕ, the Dedekind function Ψ, the sum-of-divisors function σ, or the alternating sum-of-divisors function σalt. These generalize results of Srichan and Wu.
Naveen K. Godara, Indian Institute of Technology Madras, Tamil Nadu, India-600036
(naveen.iiserb@gmail.com).
Sums of the twisted coefficients of the higher symmetric power L-functions, pp.
309–331.
ABSTRACT. Let j ≥ 2 be an integer and λsymjf(n) be the coefficients of the jth
symmetric power L-function associated with a normalized Hecke eigenform f of even
weight for the full modular group. Let σ(n) and ϕ(n) be the sum of the divisors
function and the Euler totient function, respectively. For given real numbers b
and c, we establish asymptotic formulae for the sums of the twisted arithmetic
function λsymjf2(n)σb(n)ϕc(n) over certain sparse sequences of positive integers.
As an application, we analyze the statistical properties related to the sums.
Guodong Hua, School of Mathematics and Statistics, Weinan Normal University,
Weinan, Shaaxi Province, China 714099; Research Institute of Qindong
Mathematics, Weinan Normal University, Weinan, Shaaxi Province, China 714099
(gdhuasdu@163.com).
The average distribution of Hecke eigenvalues on integral binary quadratic forms and its
applications, pp. 333–359.
ABSTRACT. Let f and g be two non-CM twist-inequivalent holomorphic cuspidal Hecke newforms, and denote its n-th normalized Fourier coefficients by λf(n) and λg(n), respectively. Let 𝒮D denotes the set of inequivalent primitive integral positive definite reduced binary quadratic form of fixed discriminant D < 0. In this paper, we prove the asymptotic estimate for the summatory function of the type
where ♭ denotes that the summation is taken over the square-free positive integers, and 𝒩 is the least common multiple of the levels of f and g. As an application, we also consider the non-trivial upper bound for the first-ever sign change of the sequence {λf(n)λg(n)}n=𝒬(x)∈𝒮D,x∈ℤ2, in terms of the analytic conductors of the associated L-functions. This work extends the previous work in this direction.
Ioana-Claudia Lazăr, Politehnica University of Timişoara, Dept. of Mathematics,
Victoriei Square 2, 300006-Timişoara, Romania (ioana.lazar@upt.ro).
Minimal displacement set for 8-located simplicial complexes with the SD’-property, pp.
361–382.
ABSTRACT. We investigate the structure of the minimal displacement set in an
8-located simplicial complex with the SD’-property. We show that such set embeds
isometrically into the complex and it is Gromov hyperbolic.
Karam Aloui, University of Tunis El Manar, Higher Institute for Medical Technologies
of Tunis, 9 Rue Zouhair Essafi 1006 Tunis and University of Sfax, laboratory of Algebra,
Geometry and Spectral Theory LR11ES53, Route de la Soukra, km 3.5 3000 Sfax,
Tunisia (karam.aloui@istmt.utm.tn).
On the average of Jordan’s function over shifted smooth numbers over sum of digits of
the squares, pp. 383–398.
ABSTRACT. We derive asymptotic estimates for some average values of the Jordan
function evaluated over shifted smooth numbers in arithmetic progressions whose sum of
digits of the square is in arithmetic progression.
C. L. Hagopian, Department of Mathematics & Statistics, California State University,
Sacramento, Sacramento,CA 95819-6051 (hagopian@csus.edu), and M. M. Marsh,
Department of Mathematics & Statistics, California State University, Sacramento,
Sacramento,CA 95819-6051 (mmarsh@csus.edu).
Some λ-connected products, pp. 399–404.
ABSTRACT. B. Knaster and S. Mazurkiewicz in 1933 defined λ-connectivity to
generalize arcwise connectivity. Unlike arcwise connectivity, a product of continua may
be λ-connected when its factors are not. We establish λ-connectivity of some products of
this type. It is not known if each product of two continua is λ-connected. Here we prove
the product of an arbitrary continuum with a continuum in which each point is contained
in a dense topological ray is λ-connected. It follows that the product of Knaster’s
buckethandle continuum and the pseudo-arc is λ-connected. Also, every product of
solenoids is λ-connected.
Gaolin Li, School of Mathematics and Statistics, Yancheng Teachers University,
Yancheng, Jiangsu, China (ligaolin1981@126.com), Chong Shen, School of Science,
Beijing University of Posts and Telecommunications, Beijing, China; Key Laboratory
of Mathematics and Information Networks (Beijing University of Posts and
Telecommunications), Ministry of Education, China (shenchong0520@163.com),
Xiaoyong Xi, School of Mathematics and Statistics, Yancheng Teachers University,
Yancheng, Jiangsu, China (xixy@yctu.edu.cn), and Dongsheng Zhao, Mathematics and
Mathematics Education, National Institute of Education, Nanyang Technological
University, 1 Nanyang Walk, Singapore 637616 (dongsheng.zhao@nie.edu.sg).
Not every T1 first-countable space is a Rudin space, pp. 405–423.
ABSTRACT. Rudin’s Lemma plays a key role in proving the major properties of quasicontinuous dcpos. Based on this lemma and its topological variant, Xu et al. (2021) introduced the concept of Rudin spaces, which provides a new link between sober spaces and well-filtered spaces, due to the recent result that a space is sober if and only if it is well-filtered and a Rudin space. It has also been confirmed that every second-countable T0 space is a Rudin space. Recently, Miao et al. constructed a first countable T0 space that is not a Rudin space. It is, however, still unknown whether every first-countable T1 space is a Rudin space. In this paper, inspired by the idea behind Isbell’s non-sober complete lattice, we construct a new countable dcpo whose Scott topology is well-filtered but not sober. As an application, we provide an example of first-countable T1 space that is not a Rudin space. Thereby, we offer a strengthened alternative resolution to the problem posed by Xu et al. (2021).