Elementary properties of factorisation. Estimate for the divisor function.
Congruence. Complete and reduced sets. The group G(H,[q]).
Field property mod P. Sums involving multiplicative functions.
Field property. Valuation function. Dirichlet diophantine approximation lemma.
Additive properties. Evaluation of . The functions τs,k(α) and Sξ,[q].
Evaluation of . Formula for r(N) in terms of S(Λ).
The equation xd=ξ over [q]. Gaussian sums. Estimation of |Sξ,[q]| and |SA,P|.
Properties of major arcs MF,G and minor arcs mF,G. Explicit determination of MF,G.
Analogue of Weyl's lemma and its application to S(A/Q).
Analogue of Hua's lemma and its application to r1(N).
Relation of S(A/Q) to SF,G and S(Λ). An important property of S(Λ).
Absolute convergence of the singular series.
Last modified 28th May 2011