论文标题
汽车汉密尔顿人，爱泼斯坦Zeta功能和Kronecker极限公式
Automorphic Hamiltonians, Epstein Zeta Functions, and Kronecker Limit Formulas
论文作者
论文摘要
首先，我们叙述了迄今为止使用自然自我接合操作员使用某些方法如何未能证明Riemann假设的历史。在第2节中，我们设定了必要的分析环境，以便在以后的部分中获得真正的证据，而不是有吸引力的启发式方法。在第3节中，我们回想起了设计的伪拉普拉斯人的实用性，通过谴责某些Eisenstein系列的Meromorphic延续，并证明了$ζ_K（s）$的间距结果，$ k $是一个复杂的二次典型领域，具有负面的决定性。在第4节中，我们构建了一个自动型哈密顿量，该自动型hamiltonian纯粹在$ l^2上具有离散的光谱（\ sl_r（\ m athbb {z}）\ backslash sl_r（\ mathbb {r}）/so（r，r，\ mathbb {r}）$，确定其基础状态，并显示出其核frun的表征。
First, we recount a history of how certain methods using natural self-adjoint operators have, thus far, failed to prove the Riemann Hypothesis. In Section 2, we set the analytical context necessary to have genuine proofs in later sections, rather than attractive heuristics. In Section 3, we recall the utility of designed pseudo-Laplacians by reproving meromorphic continuation of certain Eisenstein series and proving a spacing result for zeros of $ζ_k(s)$ for $k$ a complex quadratic field with negative determinant. In Section 4, we construct an automorphic Hamiltonian which has purely discrete spectrum on $L^2(SL_r(\mathbb{Z})\backslash SL_r (\mathbb{R})/SO(r, \mathbb{R}))$, identify its ground state, and show how it can characterize a nuclear Fréchet automorphic Schwartz space.
