Number Theory, Carbondale 1979: Proceedings of the Southern Illinois Number Theory Conference Carbondale, March 30 and 31, 1979 (Lecture Notes in Mathematics (751))

This is the third Lecture Notes volume to be produced in the framework of the New York Number Theory Seminar. The papers contained here are mainly research papers. N On certain irrational values of the logarithm....Pages 1-9 Recent results on fractional parts of polynomials....Pages 10-17 On the development of Gelfond's method....Pages 18-44 Transcendental numbers....Pages 45-69 Diophantine equations over C(t) and complex multiplication....Pages 70-81 Abhyankar's lemma and the class group....Pages 82-88 Systems of distinct representatives and minimal bases in additive number theory....Pages 89-107 Conjectures on elliptic curves over quadratic fields....Pages 108-118 Ultrafilters and combinatorial number theory....Pages 119-184 Some results related to minimal discriminants....Pages 185-194 Cyclic cubic fields that contain an integer of given index....Pages 195-199 Unique and almost unique factorization....Pages 200-205 Hecke — Weil — Jacquet — Langlands theorem revisited....Pages 206-220 Where are number fields with small class number?....Pages 221-242 Künneth formula for L-functions....Pages 243-255 The Hausdorff dimension of a set of non-normal well approximable numbers....Pages 256-264 A combinatorial problem in additive number theory....Pages 265-282 The number of bits in a product of odd integers....Pages 283-293 Prime discriminants in real quadratic fields of narrow class number one....Pages 294-301 Additive h-bases for n....Pages 302-327 A running time analysis of Brillhart's continued fraction factoring method....Pages 328-342 More than 50 mathematicians came together in Carbondale for 28 lectures on diverse topics in analytic, algebraic, additive, and combinatorial number theory. This volume contains expanded versions of many of these talks, as well as papers contributed by H. Cohn and G. V. Chudnovsky, who were unable to attend