论文标题
包装光谱（如分区功能和l/$ζ$ - 功能），以揭示本质和数量的对称性（互惠）
Packaging Spectra (as in Partition Functions and L/$ζ$-functions) to Reveal Symmetries (Reciprocity) in Nature and in Numbers
论文作者
论文摘要
在统计力学中，一个人将系统的可能能量包装到分区函数中。在数字理论和数学中的其他地方，人们将现象的频谱（例如质量数字）打包成$ζ$功能，或更普遍地纳入L功能。这些包装函数具有对称性和特性，从能量或素数本身中也不明显，例如，通常表现出比例对称性。一个人可能能够理解这些对称性并独立于实际包装来计算包装函数。因此，人们找到了一种将对象组合到一个软件包中的方法，以及辨别该软件包的对称性的方法，独立于实际包装方式。这也是Langlands计划的反复主题。在Weyl的渐近学和“听到鼓的形状”（KAC）中，包装还发现了量子电动力包装中的Schwinger Greens功能，而selberg Trace Formula中的Feynman历史总和更为普遍。
In statistical mechanics one packages the possible energies of a system into a partition function. In number theory, and elsewhere in mathematics, one packages the spectrum of a phenomenon, say the prime numbers, into a $ζ$-function or more generally into an L-function. These packaging functions have symmetries and properties not at all apparent from the energies or the primes themselves, often exhibiting scaling symmetries for example. One might be able to understand those symmetries and compute the packaging function independently of the actual packaging. And so one finds a way of putting together objects into a package, and ways of discerning symmetries of that package independent of the actual mode of packaging. This is a recurrent theme of the Langlands Program as well. Packaging is also found in Weyl's asymptotics and "hearing the shape of a drum" (Kac), the Schwinger Greens function in quantum electrodynamics packaging the Feynman sum of histories, and more generally in the Selberg trace formula.
