discipline

Pure Mathematics

subject

Additive Number Theory

lecturers

András Sárközy

credits

2

period

 

curriculum

The Hardy-Littlewood method in general. The odd Goldbach-problem. Large arcs, singular series. Small arcs, the Vaughan method, lemmata of Vinogradov-Vaughan and of Vinogradov. Outline of the even Goldbach-problem. Waring’s problem. Weyl-sums, Weyl-method, Weyl-shift. Two lemmata by Weyl, Weyl-inequality, the difference operator. Hua’s lemma. The contribution of small arcs. The contribution of large arcs depending on the singular series and integral (with sketch of proof). Roth’s theorem for 3-term arithmetic progressions. Squares in difference sequences (outline). Representation as the sum of 3 “smooth” numbers (outline).

literature

 

form of tuition

Lecture

mode of assessment

written/oral exam