Let K be a field of characteristic 0 and let n be a natural number. Let Γ be a subgroup of the multiplicative group (K*) n of finite rank r. Given a1,..., an ∈ K* write A(a1,..., an, Γ) for the number ...

Some important points to revise from the chapter are: • An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in ...

Grade school math students are likely familiar with teachers admonishing them not to just guess the answer to a problem. But a new proof establishes that, in fact, the right kind of guessing is ...