Open University of Cyprus

Frobenius minimality of the Huneke-Wiegand counterexample in symmetric numerical semigroup rings

Son Pham publicly identified a counterexample to the Huneke-Wiegand conjecture in the class of two-generated monomial ideals over symmetric numerical semigroup rings, subsequently verified independently by Professor Craig Huneke. This preprint preserves that discovery priority an...

The bottom of the Shub-Smale tau conjecture: an exact census of integer roots for constant-free straight-line programs of length at most seven

For a univariate integer polynomial f, let tau(f) be the minimum number of +,-,x gates needed to compute f from x and the constants -1,0,1, and let z(f) be its number of distinct integer roots. The Shub-Smale tau conjecture (Smale's fourth problem) asserts z(f) ≤ (1+tau(f))^k for...

The bottom of the Shub-Smale tau conjecture: an exact census of integer roots for constant-free straight-line programs of length at most seven

For a univariate integer polynomial f, let tau(f) be the minimum number of +,-,x gates needed to compute f from x and the constants -1,0,1, and let z(f) be its number of distinct integer roots. The Shub-Smale tau conjecture (Smale's fourth problem) asserts z(f) ≤ (1+tau(f))^k for...