A notebook of claims, arguments and the evidence behind them. Read the manuscript with a roadmap, inspect its prerequisites, and compare your assessment with the referee panel.
The manuscript proposes a uniform zero-free region for finite-order Hecke L-functions over Q(√−3) and for Dirichlet L-functions, including the Riemann zeta function. Its argument passes from cubic theta reflection and Poisson expansion through two moment reductions to the final half-plane.
The manuscript derives facet and product identities for projection-body volume, calculates the simplex benchmark, and compares a product of simplex factors with that benchmark. A final corollary studies dimension-dependent growth.
The manuscript defines a polynomial from a cusp relation and a shifted auxiliary algebra. A local lifting lemma identifies its zero-fibre quotient with a polynomial extension of a two-variable ring. An ambient polynomial identity supplies a critical point on another fibre, and a Jacobian argument is used to rule out a coordinate. Adjoining variables gives the higher-dimensional statements; the appendix records both coordinate maps.
The manuscript expresses the specified canonical map as multiplication in an invariant tensor algebra. An annihilator criterion reduces surjectivity to vanishing of symmetric multilinear forms on products. A directional-derivative injectivity lemma and two differentiation sequences surround an induction on the number of slots, yielding the stated degree range. Complete reducibility then supplies a representation embedding in the opposite direction.
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