Robert P. Langlands

Author's comments: The following brief discourse was delivered in Erlangen in October 2004, on the occasion of the award of the Karl Georg Christian von Staudt-Preis to Günter Harder. It does not do justice to his many contributions to mathematics, but does attempt to express my great admiration of him and my great respect for the passion and the tenacity with which he continues to reflect on what seem to me some of the central problems of the modern theory of numbers.

Authors's comments: These are my responses to questions of Farzin Barekat, a graduate student at the University of British Columbia, where I was an undergraduate student for four years and a graduate student for one year. The questions and my responses were transmitted electronically. An abbreviated version of my responses will be published in a newsletter of the mathematics department of the university.

Solomon Bochner in his office at Rice University
(Photograph courtesy of William Veech and the Rice University Archives, Woodson Research Center)

Author's comments: This note contains a few recollections of a year I spent in Turkey in 1967/68, where my office was adjacent to that of Cahit Arf, known, among other things, for the Hasse-Arf theorem and the Arf invariant. It was he who referred me---as I was first attempting to define local $\epsilon$-factors for Artin $L$-functions---to the paper of Hasse published in the Acta Salmanticensia. Hasse's paper was my first introduction to the methods that had already been introduced for calculating and comparing the $\epsilon$-factors.