A structure theorem for sets of lengths
We prove that every set A ⊂ ℤ satisfying for t and δ in suitable ranges must be very close to an arithmetic progression. We use this result to improve the estimates of Green and Morris for the probability that a random subset A ⊂ ℕ satisfies |ℕ∖(A+A)| ≥ k; specifically, we show that .
Let be the error term in the mean square formula of the Riemann zeta-function in the critical strip . It is an analogue of the classical error term . The research of has a long history but the investigation of is quite new. In particular there is only a few information known about for . As an exploration, we study its mean value . In this paper, we give it an Atkinson-type series expansion and explore many of its properties as a function of .
In Computer Algebra, Subresultant Theory provides a powerful method to construct algorithms solving problems for polynomials in one variable in an optimal way. So, using this method we can compute the greatest common divisor of two polynomials in one variable with integer coefficients avoiding the exponential growth of the coefficients that will appear if we use the Euclidean Algorithm.In this note, generalizing a forgotten construction appearing in [Hab], we extend the Subresultant Theory to the...
We give a survey of computational class field theory. We first explain how to compute ray class groups and discriminants of the corresponding ray class fields. We then explain the three main methods in use for computing an equation for the class fields themselves: Kummer theory, Stark units and complex multiplication. Using these techniques we can construct many new number fields, including fields of very small root discriminant.
In this survey article we start from the famous Furstenberg theorem on non-lacunary semigroups of integers, and next we present its generalizations and some related results.