标题： 黎曼ζ函数的量化与宇宙学 显示英文标题

标题： Quantization of the Riemann Zeta-Function and Cosmology

摘要： 提出黎曼zeta函数的量化方法。 我们将黎曼zeta函数视为一个伪微分算子的符号，并研究相应的经典和量子场论。 这种方法的动机来自于p进弦理论以及对弦状宇宙模型的最新研究。 我们表明，zeta函数场的拉格朗日量等价于质量由黎曼zeta函数零点定义的克莱因-戈登拉格朗日量的总和。 指出费马-怀尔斯数学和兰兰德纲领的量化。 贝林森关于动机L函数值的猜想被解释为涉及宇宙常数问题。 讨论了zeta函数场论可能的宇宙学应用。 显示英文摘要

摘要： Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories. This approach is motivated by the theory of p-adic strings and by recent works on stringy cosmological models. We show that the Lagrangian for the zeta-function field is equivalent to the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of the Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and the Langlands program is indicated. The Beilinson conjectures on the values of L-functions of motives are interpreted as dealing with the cosmological constant problem. Possible cosmological applications of the zeta-function field theory are discussed.