I came to Illinois in the Great Migration of the 1960s, as part of the expansion and renewal of the Illinois Math Department. In my case the attraction was neither the scenery nor the climate, but the presence of Paul Bateman. We shared interests in prime numbers, tauberian and oscillation theorems, and several other topics. Paul had a significant effect on me and many others, through his interest, activity and broad knowledge.
Paul always had projects going, and I became a part of many of them. These included organizing conferences, jointly writing half-a-dozen articles and a book on analytic number theory  completed when Paul was 85 years old, and taking on a 5-year stint as co-editors of the Problem Section of the American Mathematical Monthly. Paul was not one to palm off unpleasant work on junior partners — for the editorship, for example, he did all the large amount of work of writing to authors and referees, and I just studied the suitability of proposed problems, which was much more fun. He was very proud of our having cleaned up a backlog of unsolved problems and, as he put it, of “keeping egg off our faces.”
While preparing a survey article on , Paul and I developed a conjecture that the prime number theorem for these numbers held under an \( L^2 \) hypothesis weaker than Beurling’s famous pointwise condition. This conjecture was proved some 30 years later by in a series of impressive articles, which were cited in his election as a full member of the French Academy of Sciences in 1998.generalized numbers
Along with his other colleagues and friends, I will remember Paul for his guidance, support, encouragement, and friendship.