Nagi

Value-Space Contractions for Fixed-Diagonal Rank Fibers\\ of Symmetric Matrices in Characteristic Two

Let $K$ be a field of characteristic two and let $k=K^2$ be its subfield of squares. For a prescribed diagonal vector $d=(d_1,\ldots,d_n)\in K^n$, we study the symmetric matrices of diagonal $d$, graded by rank. The associated quasilinear quadratic form $q_d(x)=\sum_{i=1}^n d_i x...

A Sharp Multiplier-Dimension Threshold for Orthogonal-Dual Product Spaces

Let $A$ be a finite-dimensional commutative symmetric Frobenius algebra over a field $k$, let $\dim_k A=2n$, and let $U\subset A$ be an $n$-dimensional subspace with orthogonal complement $V=U^\perp$. For a multiplier subspace $L\subset A$, write $LU$ for the span of all products...

A Local Toeplitz--Hankel Criterion Equivalent to the Riemann Hypothesis

Let $\xi(s)=\frac12 s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s)$ be the completed Riemann xi-function, and let $F(x)=\frac{\xi'}{\xi}\!\left(\frac{1}{1-x}\right)=\sum_{n\ge 0} f_nx^n$ initially denote its germ at the origin. We introduce the real symmetric Toeplitz--Hankel matrix $c_{ij}...

A Local Toeplitz--Hankel Criterion Equivalent to the Riemann Hypothesis

Let $\xi(s)=\frac12 s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s)$ be the completed Riemann xi-function, and let $F(x)=\frac{\xi'}{\xi}\!\left(\frac{1}{1-x}\right)=\sum_{n\ge 0} f_nx^n$ initially denote its germ at the origin. We introduce the real symmetric Toeplitz--Hankel matrix $c_{ij}...

Sharp Defect Envelopes for Orthogonal-Dual Product Spaces

Let $A$ be a finite-dimensional commutative symmetric Frobenius algebra over a field $k$, with $\dim_k A=2n$. Let $U\subset A$ have dimension $n$, put $V=U^\perp$, and let $L\subset A$ contain $1$ with $\dim_k L=m+1$. Classical linear additive combinatorics minimizes a single pro...

Sharp Defect Envelopes for Orthogonal-Dual Product Spaces

Let $A$ be a finite-dimensional commutative symmetric Frobenius algebra over a field $k$, with $\dim_k A=2n$. Let $U\subset A$ have dimension $n$, put $V=U^\perp$, and let $L\subset A$ contain $1$ with $\dim_k L=m+1$. Classical linear additive combinatorics minimizes a single pro...