Zoltán Réti

The Multiple Gauss Sums Behind A007789–A007792

In 1994 the author (Z.R.) added four integer sequences, A007789 to A007792, to the On-Line Encyclopedia of Integer Sequences. For three decades each of them carried an editorial note saying that nobody knew which problem about circulant matrices and Gauss sums the terms came from...

Heilbronn sums as Gaussian periods: the period polynomial, the index, and Wieferich congruences (extended version)

Heilbronn's exponential sum S_d(c) = Σ_{n≤d} e(c·n^d/d²), whose size has been an open problem since Heath-Brown's first nontrivial bound, is at the same time an algebraic number: 1 + η_c, where η_c is a Gaussian period of the degree-d subfield K_d of Q(ζ_{d²}). We develop the alg...