加权重数函数的均方

关于素数分解中加权平均重数的一个注记

A remark on weighted average multiplicities in prime factorisation

本文推广ABC三元组的质量定义，引入加权平均重数（WAM），证明其实部小于1时无界、大于1时全纯有界，并揭示其与最大素因子重数及ABC猜想的联系。

On distinguished square-integrable representations for Galois pairs and a conjecture of Prasad

We prove an integral formula computing multiplicities of square-integrable representations relative to Galois pairs over $p$-adic fields and we apply this formula to verify two consequences of a conjecture of Dipendra Prasad. One concerns the exact computation of the multiplicity of the Steinberg representation and the other the invariance of multiplicities by transfer among inner forms.

同余曲面上闭测地线的一个中值定理

A Mean Value Theorem for Closed Geodesics on Congruence Surfaces

本文对有限面积黎曼曲面上给定长度的闭测地线定义了一个加权重数函数。这些加权的多重性自然出现在塞尔伯格迹公式，特别是他们的均方起着重要的作用，在研究统计的特征值的表面上的拉普拉斯算子。在模域的情况下，E. Bogomolny，F. Leyvraz和C.施米特给出了一个均方公式，M.彼得本文计算了有理四元数代数单位群的同余子群所对应的曲面的加权重数的均方，特别是模群的同余子群的加权重数的均方.值得注意的是，结果是模域均方的有理倍数。

长度谱中的重数与 Salem 数的增长率

Multiplicities in the length spectrum and growth rate of Salem numbers

本文研究非紧算术双曲轨形长度谱平均重数的指数增长，借助可开平方 Salem 数推广偶数维结果，并用其分布渐近式说明方法估计的最优性。

A Local Trace Formula for the Generalized Shalika Model

We study local multiplicities associated to the so-called generalized Shalika models. By establishing a local trace formula for these kind of models, we are able to prove a multiplicity formula for discrete series. As a result, we can show that these multiplicities are constant over every discrete Vogan $L$-packet and that they are related to local exterior square $L$-functions.

Families of modular arithmetic progressions with an interval of distance multiplicities

Given a family $\mathcal{F}=\{A_1,\dots,A_s\}$ of subsets of $\mathbb{Z}_n$, define $Δ\mathcal{F}$ to be the multiset of all (cyclic) distances dist$(x,y)$, where $\{x,y\} \subset A_i$, $x \neq y$, for some $i=1,\dots,s$. Taking inspiration from a Euclidean distance problem of Erdős, we say that $\mathcal{F}$ is Erdős-deep if the multiplicities of distances that occur in $Δ\mathcal{F}$ are precisely $1,2,\dots,k-1$ for some integer $k$. In the case $s=1$, it is known that a modular arithmetic progression in $\mathbb{Z}_n$ achieves this property (under mild conditions); conversely, APs are the …