Primes, Diophantine equations, and algebraic number theory.
A new twisted function-field version of Chowla's conjecture yields the required density-zero bound for irreducible non-$S_n$ polynomials in every degree $n \geq 40$.
Rank-2 log-unit lattices encode Galois structure and, for totally imaginary non-CM D6 sextics, determine the underlying field.
Arithmetic level-d estimates, sieve-based exponential sums, and random sparsification yield a stretched-exponential upper bound for every exponent below 1/2.
Decision trees expose explicit formulas for three reduced minimal coefficients using traces at 2 and 3 plus conductor parity.
