Related papers: Note on the additive complements of primes

We extend a recent result of Khalfalah and Szemeredi to the polynomials of prime variables.

We say the sets of nonnegative integers A and B are additive complements if their sum contains all sufficiently large integers. In this paper we prove a conjecture of Chen and Fang about additive complement of a finite set.

Two infinite sequences A and B of non-negative integers are called additive complements, if their sum contains all sufficiently large integers. Let $A(x)$ and $B(x)$ be the counting functions of A and B. In this paper, we extend the results…

The following article is one of introduction to additive frieze patterns, linking the subject to multiplicative frieze patterns. We also add two new theorems about additive frieze patterns (see theorem 2 and 5) and a conjecture about…

Under the prime-tuple hypothesis, the set of signed primes is a sumset.

A survey paper on some recent results on additive problems with prime powers.

We unify in a large class of additive functions the results obtained in the first part of this work. The proof rests on series involving the Riemann zeta function and certain sums of primes which may have their own interest.

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

We modify the proof of the basic lemma of a paper of Saks and Zygmund on additive functions of rectangles.

The number of finite additive 2-bases is known to grow exponentially. While this fact has been established by Marzuola and Miller (2010) using complex analytic techniques embedded in the study of numerical sets, we provide a direct, short…

We give a more strong heuristic justification of our conjecture on the excess of the odious primes.

We confirm several conjectures of Guo, Jouhet and Zeng concerning the factors of alternative binomials sums.

We continue our recent work on averages for ternary additive problems with powers of prime numbers.

Addendum to the paper Combinatorics of the Modular Group II The Kontsevich integrals, hep-th/9201001, by C. Itzykson and J.-B. Zuber (3 pages)

Supplementary results obtained after the completion of our previous paper are given together with discussing some examples. A quick review of the previous paper is also included.

Best possible bounds are obtained for the concentration function of an additive arithmetic function on sequences of shifted primes.

We prove some extensions of Andrews inequality.

In the present work the existence of some patterns of primes is shown which generalize the celebrated result of Green and Tao according to which there are arbitrarily long arithmetic progressions in the sequence of primes

We study an extension of Montgomery's pair-correlation conjecture and its relevance in some problems on the distribution of prime numbers.

We use the methods developed in our papers on moments and divisor correlations to derive heuristically the conjectural ratios formula for two zetas over two zetas.