A Theorem on Analytic Strong Multiplicity One

Let $K$ be an algebraic number field, and $\pi=\otimes\pi_{v}$ an irreducible, automorphic, cuspidal representation of \GL_{m}(\mathbb{A}_{K}) with analytic conductor $C(\pi)$. The theorem on analytic strong multiplicity one established in this note states, essentially, that there exists a positive constant $c$ depending on $\varepsilon>0, m,$ and $K$ only, such that $\pi$ can be decided completely by its local components $\pi_{v}$ with norm $N(v)<c\cdot C(\pi)^{2m+\varepsilon}.$Comment: accepted by J. Number Theor

On a conjecture of Montgomery-Vaughan on extreme values of automorphic L-functions at 1

A first version of this paper previously circulated under the title "Distribution function of values of random Euler products at 1".In this paper, we prove a weaker form of a conjecture of Montgomery-Vaughan on extreme values of automorphic L-functions at 1

On a certain non-split cubic surface

In this note, we establish an asymptotic formula for the number of rational points of bounded height on the singular cubic surface $$x_0(x_1^2 + x_2^2)=x_3^3$$ with a power-saving error term, which verifies the Manin-Peyre conjectures for this surface.Comment: v2. 18 pages, one author adde

Construction health and safety: A topic landscape study

We aim to draw in-depth insights into the current literature in construction health and safety and provide perspectives for future research efforts. The existing literature on construction health and safety is not only diverse and rich in sight, but also complex and fragmented in structure. It is essential for the construction industry and research community to understand the overall development and existing challenges of construction health and safety to adapt to future new code of practice and challenges in this field. We mapped the topic landscape followed by identifying the salient development trajectories of this research area over time. We used the topic modeling algorithm to extract 10 distinct topics from 662 abstracts (filtered from a total of 895) of articles published between 1991 and 2020. In addition, we provided the most cited references and the most popular journal per topic as well. The results from a time series analysis suggested that the construction health and safety would maintain its popularity in the next 5 years. Research efforts would be devoted to the topics including “Physical health and disease”, “Migrant and race”, “Vocational ability and training”, and “Smart devices.” Among these topics, “Smart devices” would be the most promising one