Lethbridge Number Theory and Combinatorics Seminar: Tim Trudgian

Very little is known about the distribution of primitive roots of a prime p. Grosswald conjectured that the least primitive root of a prime p is less than the square root of p, minus 2, for all p greater than 409. While this is certainly true for all p sufficiently large, Grosswald's conjecture in still open. I shall outline some recent work which resolves the conjecture completely under the Generalised Riemann Hypothesis and which almost resolves the conjecture unconditionally.