Zhuo Chen

Angular Monotonicity of Completed Dirichlet L-Functions via the Three-Term Zeta Decomposition: A Proof of the Generalized Riemann Hypothesis for Non-Principal Characters

Version 6, 2026-08-31. This version adds links to the companion interactive web pages (English/Chinese expository sites) and the GitHub code repository. No mathematical content changes from v5. We prove the Generalized Riemann Hypothesis (GRH) for all non-principal Dirichlet L-fu...

Quantum Chaos of Arithmetic Origin

v3 changelog: Added §7.4 OTOC (out-of-time-order correlator) dynamical non-integrability evidence; added §6 Discussion: three conceptual implications (third route to quantum chaos; correlational structure of matrix elements; structural correspondence beyond statistical analogy)....

Angular Monotonicity of Completed Dirichlet L-Functions via the Three-Term Zeta Decomposition: A Proof of the Generalized Riemann Hypothesis for Non-Principal Characters

We prove the Generalized Riemann Hypothesis (GRH) for all non-principal Dirichlet L-functions L(s,chi) with conductor q >= 3. The proof proceeds by combining the three-term polylogarithm decomposition of the Riemann zeta function with the completed L-function Lambda(s,chi) to for...

Quantum Chaos of Arithmetic Origin: Deterministic L-function Jacobi Hamiltonians exhibit GUE/GOE level statistics without random disorder or classical chaos

We construct explicit one-dimensional tight-binding (Jacobi) Hamiltonians whose recurrence coefficients are generated purely from the arithmetic of completed L-functions (Riemann zeta, Dirichlet beta, Ramanujan delta), via circle sampling, Hausdorff moments of the log-derivative...

Quantum Chaos of Arithmetic Origin: Deterministic L-function Jacobi Hamiltonians exhibit GUE/GOE level statistics without random disorder or classical chaos (v2)

We construct explicit one-dimensional tight-binding (Jacobi) Hamiltonians whose recurrence coefficients are generated purely from the arithmetic of completed L-functions (Riemann zeta, Dirichlet beta, Ramanujan delta), via circle sampling, moments of the log-derivative Taylor coe...

Quantum Chaos of Arithmetic Origin: Deterministic L-function Jacobi Hamiltonians exhibit GUE/GOE level statistics without random disorder or classical chaos

We construct explicit one-dimensional tight-binding (Jacobi) Hamiltonians whose recurrence coefficients are generated purely from the arithmetic of completed L-functions (Riemann zeta, Dirichlet beta, Ramanujan delta), via circle sampling, Hausdorff moments of the log-derivative...

Proof of the Generalized Riemann Hypothesis via Angular Monotonicity of the Completed L-function

We prove the Generalized Riemann Hypothesis (GRH) for all non-principal Dirichlet L-functions L(s,chi) with conductor q >= 3. The proof proceeds by combining the three-term polylogarithm decomposition of the Riemann zeta function with the completed L-function Lambda(s,chi) to for...

Proof of the Generalized Riemann Hypothesis via Angular Monotonicity of the Completed L-function

We prove the Generalized Riemann Hypothesis (GRH) for all non-principal Dirichlet L-functions L(s,chi) with conductor q >= 3. The proof proceeds by combining the three-term polylogarithm decomposition of the Riemann zeta function with the completed L-function Lambda(s,chi) to for...