Tao Lin

Canonical bounded pair defects for roots of quadratic congruences

Let f in Z[x] be an irreducible quadratic polynomial and let A_{q,f}(X) count solutions of f(n) = 0 mod q in 1 <= n <= X.For an unramified odd prime power q, the local root system contains either zero or two residues per period.We study the dyadic pair-count defect binom(A_{q,f}(...

Canonical bounded pair defects for roots of quadratic congruences

Let f in Z[x] be an irreducible quadratic polynomial and let A_{q,f}(X) count solutions of f(n) = 0 mod q in 1 <= n <= X.For an unramified odd prime power q, the local root system contains either zero or two residues per period.We study the dyadic pair-count defect binom(A_{q,f}(...

Minkowski Bounds for Pasten's Arithmetic Derivative Lattices in the Squarefree Subfamily

This preprint studies the squarefree subfamily of the arithmetic-derivative lattices introduced by Hector Pasten. It proves an exact determinant identity and combines it with Vaaler's subspace lattice theorem to obtain explicit lattice-vector bounds. It further develops a structu...

Structural Lemmas for the First-Prime Window of the Weil Quadratic Form

We prove six structural results for the local Weil quadratic form Q_W^L on L^2(-L,L) in the first-prime window (half*log2 < L < half*log3), the minimal interval where only the prime n=2 contributes to the Weil explicit formula. Our main technical contribution (Theorem 5.1) is an...