Arithmetic progressions in sumsets

Imre Z. Ruzsa

Displaying similar documents to “Arithmetic progressions in sumsets”

Multiplicative functions of polynomial values in short intervals

Mohan Nair (1992)

Acta Arithmetica

Similarity:

On the number of representations in the Waring-Goldbach problem with a prime variable in an arithmetic progression

Maurizio Laporta (2012)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We prove a Bombieri-Vinogradov type theorem for the number of representations of an integer $N$ in the form $N = p_{1}^{g} + p_{2}^{g} + ... + p_{s}^{g}$ with $p_{1}, p_{2}, ..., p_{s}$ prime numbers such that $p_{1} \equiv l (\mod k)$ , under suitable hypothesis on $s = s (g)$ for every integer $g \geq 2$ .

On a problem of Matkowski

Zoltán Daróczy, Gyula Maksa (1999)

Colloquium Mathematicae

Similarity:

We solve Matkowski's problem for strictly comparable quasi-arithmetic means.

Irrationality measures of the values of hypergeometric functions

Masayoshi Hata (1992)

Acta Arithmetica

Similarity:

Extremes of interarrival times of a Poisson process under conditioning

A. Abay (1995)

Applicationes Mathematicae

Similarity:

On the counting function for the generalized Niven numbers

Ryan Daileda, Jessica Jou, Robert Lemke-Oliver, Elizabeth Rossolimo, Enrique Treviño (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Given an integer base $q \geq 2$ and a completely $q$ -additive arithmetic function $f$ taking integer values, we deduce an asymptotic expression for the counting function $N_{f} (x) = # \{0 \leq n < x | f (n) ∣ n\}$ under a mild restriction on the values of $f$ . When $f = s_{q}$ , the base $q$ sum of digits function, the integers counted by $N_{f}$ are the so-called base $q$ Niven numbers, and our result provides a generalization of the asymptotic known in that case.

Lower bounds for a certain class of error functions

J. Herzog, P. R. Smith (1992)

Acta Arithmetica

Similarity:

Large sets with small doubling modulo $p$ are well covered by an arithmetic progression

Oriol Serra, Gilles Zémor (2009)

Annales de l’institut Fourier

Similarity:

We prove that there is a small but fixed positive integer $ϵ$ such that for every prime $p$ larger than a fixed integer, every subset $S$ of the integers modulo $p$ which satisfies $| 2 S | \leq (2 + ϵ) | S |$ and $2 (| 2 S |) - 2 | S | + 3 \leq p$ is contained in an arithmetic progression of length $| 2 S | - | S | + 1$ . This is the first result of this nature which places no unnecessary restrictions on the size of $S$ .