Enrico Bombieri

Around the Davenport-Heilbronn Function

Enrico Bombieri
Institute for Advanced Study
November 10, 2011

The Davenport-Heilbronn function (introduced by Titchmarsh) is a linear combination of the two L-functions with a complex character mod 5, with a functional equation of L-function type but for which the analogue of the Riemann hypothesis fails. In this lecture, we study the Moebius inversion for functions of this type and show how its behavior is related to the distribution of zeros in the half-plane of absolute convergence. Work in collaboration with Amit Ghosh.

The Mathematical Truth

Enrico Bombieri
Institute for Advanced Study
October 29, 2010

In this lecture, Enrico Bombieri, IBM von Neumann Professor in the School of

Mathematics, attempts to give an idea of the numerous different notions of truth in mathematics. Using accessible examples, he explains the difference between truth, proof, and verification. Bombieri, one of the world’s leading authorities on number theory and analysis, was awarded the Fields Medal in 1974 for his work on the large sieve and its application to the distribution of prime numbers. Some of his work has potential practical applications to cryptography and security of data transmission and identification.

The Mathematical Infinity

Enrico Bombieri
Institute for Advanced Study
January 31, 2007

VaseThis lecture by Enrico Bombieri, IBM von Neumann Professor in the School of Mathematics, explores how mathematics has arrived at its present pragmatic view of infinity and some of the counterintuitive paradoxes, as well as some of the positive results, deriving from its acceptance. It concludes with a view of how computer science is leading today to a new precise concept, namely the impossibly large in the realm of the finite.