Computation and the Riemann Hypothesis: Dedicated to Herman te Riele on the occasion of his retirement Andrew Odlyzko School of Mathematics University of Minnesota
[email protected] http://www.dtc.umn.edu/∼odlyzko December 2, 2011 Andrew Odlyzko ( School of Mathematics UniversityComputation of Minnesota and
[email protected] Riemann Hypothesis: http://www.dtc.umn.edu/ Dedicated toDecember2,2011 Herman te∼ Rieodlyzkole on) the 1/15 occasion The mysteries of prime numbers: Mathematicians have tried in vain to discover some order in the sequence of prime numbers but we have every reason to believe that there are some mysteries which the human mind will never penetrate. To convince ourselves, we have only to cast a glance at tables of primes (which some have constructed to values beyond 100,000) and we should perceive that there reigns neither order nor rule. Euler, 1751 Andrew Odlyzko ( School of Mathematics UniversityComputation of Minnesota and
[email protected] Riemann Hypothesis: http://www.dtc.umn.edu/ Dedicated toDecember2,2011 Herman te∼ Rieodlyzkole on) the 2/15 occasion Herman te Riele’s contributions towards elucidating some of the mysteries of primes: numerical verifications of Riemann Hypothesis (RH) improved bounds in counterexamples to the π(x) < Li(x) conjecture disproof and improved lower bounds for Mertens conjecture improved bounds for de Bruijn – Newman constant ... Andrew Odlyzko ( School of Mathematics UniversityComputation of Minnesota and
[email protected] Riemann Hypothesis: http://www.dtc.umn.edu/ Dedicated toDecember2,2011