Number Theory, Carbondale 1979 Proceedings of the Southern Illinois Number Theory Conference Carbondale, March 30 and 31, 1979

On certain irrational values of the logarithm.- Recent results on fractional parts of polynomials.- On the development of Gelfond's method.- Transcendental numbers.- Diophantine equations over ?(t) and complex multiplication.- Abhyankar's lemma and the class group.- Systems of distinct representatives and minimal bases in additive number theory.- Conjectures on elliptic curves over quadratic fields.- Ultrafilters and combinatorial number theory.- Some results related to minimal discriminants.- Cyclic cubic fields that contain an integer of given index.- Unique and almost unique factorization.- Hecke - Weil - Jacquet - Langlands theorem revisited.- Where are number fields with small class number?.- Künneth formula for L-functions.- The Hausdorff dimension of a set of non-normal well approximable numbers.- A combinatorial problem in additive number theory.- The number of bits in a product of odd integers.- Prime discriminants in real quadratic fields of narrow class number one.- Additive h-bases for n.- A running time analysis of Brillhart's continued fraction factoring method.