Algebra & Number Theory Seminar | Department Home
Texas Tech University
Title: Beukers' proof of irrationality of ζ(3) and Brown's program of irrationality proofs for zeta values.
Abstract: In 1978, Roger Apery produced a sensation when he proved the irrationality of ζ(3). Later, Frits Beukers gave two reinterpretations of Apery's proof; the first one uses iterated integrals and Legendre polynomials and the second one uses modular forms. In this talk, we shall present the first one and we also give an account into Brown's program of irrationality proofs for zeta values. Brown's main idea is a common geometric framework where period integrals play a special role in understanding these irrationality proofs. It was proved by Brown that these integrals are ℚ-linear combinations of multiple zeta values of a given weight.