Intersective sets given by a polynomial
Inverse Additive Number Theory. XI. Long arithmetic progressions in sets with small sumsets
Inverse zero-sum problems
Inverse zero-sum problems and algebraic invariants
Inverse zero-sum problems {II}
Inverse zero-sum problems {III}
Inverse zero-sum problems in finite Abelian p-groups
We study the minimal number of elements of maximal order occurring in a zero-sumfree sequence over a finite Abelian p-group. For this purpose, and in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, our method implies that, if we denote by exp(G) the exponent of the finite Abelian p-group G considered, every zero-sumfree sequence S with maximal possible length over...
Kneser’s theorem for upper Banach density
Suppose is a set of non-negative integers with upper Banach density (see definition below) and the upper Banach density of is less than . We characterize the structure of by showing the following: There is a positive integer and a set , which is the union of arithmetic sequences [We call a set of the form an arithmetic sequence of difference and call a set of the form an arithmetic progression of difference . So an arithmetic progression is finite and an arithmetic sequence...
Kombinatorik mit dem Computer: Klassifikationen und damit verwandte Figuren.
La «nouvelle technique» de Hooley
Lagrange's Four Squares Theorem with almost prime variables.
Landau’s problems on primes
At the 1912 Cambridge International Congress Landau listed four basic problems about primes. These problems were characterised in his speech as “unattackable at the present state of science”. The problems were the following :(1)Are there infinitely many primes of the form ?(2)The (Binary) Goldbach Conjecture, that every even number exceeding 2 can be written as the sum of two primes.(3)The Twin Prime Conjecture.(4)Does there exist always at least one prime between neighbouring squares?All these...
Large sets with small doubling modulo are well covered by an arithmetic progression
We prove that there is a small but fixed positive integer such that for every prime larger than a fixed integer, every subset of the integers modulo which satisfies and is contained in an arithmetic progression of length . This is the first result of this nature which places no unnecessary restrictions on the size of .
Lattice point problems and distribution of values of quadratic forms.
Lattice point problems and the central limit theorem in Euclidean spaces.
Lattice Point Theory of Irrational Ellipsoids with an Arbitrary Center.
Lattice Points.
Lattice points in a circle: An improved mean-square asymptotics
Lattice Points in a Circle and Divisors in Arithmetic Progressions.
Lattice points in bodies of revolution