New York Number Theory Seminar
February 20, 2003, 3:30 PM in Room 5417
- Speaker:
- Mel Nathanson (CUNY Lehman College)
- Title:
- Generalized additive bases, Konig's lemma, and the Erdos-Turan
conjecture
- Abstract:
- This paper introduces a new class of additive bases and a
genaral additive problem, a special case of which is the Erdos-Turan
conjecture that the representation function of a basis of order 2 cannot
be bounded. Konig's lemma on the existence of infinite paths in certain
graphs is used to prove that the general additive problem for infinite
sets is equaivalent to a related problem about finite sets. Other new
results about the representation functions of additive bases will also be
discussed.