Arithmetic progressions in sums of subsets of sparse sets
Arithmetic progressions in sumsets
1. Introduction. Let A,B ⊂ [1,N] be sets of integers, |A|=|B|=cN. Bourgain [2] proved that A+B always contains an arithmetic progression of length . Our aim is to show that this is not very far from the best possible. Theorem 1. Let ε be a positive number. For every prime p > p₀(ε) there is a symmetric set A of residues mod p such that |A| > (1/2-ε)p and A + A contains no arithmetic progression of length (1.1). A set of residues can be used to get a set of integers in an obvious way. Observe...
Arithmetic progressions of prime-almost-prime twins
Arithmetic properties for hyper -ary partition functions.
Arithmetic properties of overpartition pairs
Arithmetical applications of an identity for the Vandermonde determinant
Arithmetical consequences of two identities of B. Gordon.
Arithmetical notes, IX. On the set of integers representable as a product of a prime and square
Arithmetical properties of finite rings and algebras, and analytic number theory.
Arithmetical properties of finite rings and algebras, and analytic number theory. II.
Asymptotic analysis of Ramanujan pairs.
Asymptotic analysis of Ramanujan pairs. (Short Communication).
Asymptotic density in combined number systems.
Asymptotic Formula for Distinct Partitions of Lattice Points with Congruence Restrictions.
Asymptotic formulae for partition ranks
Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F. Dyson and recently proved by the first author and K. Bringmann.
Asymptotic formulas and generalized Dedekind sums.
Asymptotique des récurrences mahlériennes : le cas cyclotomique
Nous étudions le comportement asymptotique d’une classe de suites mahlériennes dont les séries génératrices sont des produits infinis. Un exemple caractéristique est celui de l’estimation des coefficients de Taylor de , voisin des partitions binaires étudiées par De Bruijn. Le résultat obtenu illustre un cas typique d’une classification naturelle des suites mahlériennes. Les techniques utilisées, transformation de Mellin ou méthode du col, ressortissent à la théorie analytique des nombres et à...
Asymptotische Aussagen über Partitionen.
Asymptotische Formeln für Partitionen.
Average Frobenius distribution of elliptic curves