Related papers: Note on the additive complements of primes
In a recent article, Apagodu and Zeilberger (http://arxiv.org/abs/1606.03351)discuss some applications of an algorithm for finding and proving congruence identities (modulo primes) of indefinite sums of many combinatorial sequence. At the…
The polynomial Fre\u{\i}man--Ruzsa conjecture is a fundamental open question in additive combinatorics. However, over the integers (or more generally $\mathbb{R}^d$ or $\mathbb{Z}^d$) the optimal formulation has not been fully pinned down.…
A short comment about a recent note by Kiss and Sandor on the maximum values of additive representation functions.
We show that a positive proportion of all gaps between consecutive primes are small gaps. We provide several quantitative results, some unconditional and some conditional, in this flavour.
In the recent article arXiv:1606.03351, Apagodu and Zeilberger discuss some applications of an algorithm for finding and proving congruence identities (modulo primes) of indefinite sums of many combinatorial sequence. At the end they…
In the conference paper we construct analouge to Pascal's triangle that characterize primes with additional fascinating properties.
In this article we prove level raising for cuspidal eigenforms modulo prime powers (for odd primes) of weight $k\geq 2$ and arbitrary character, extending the result in weight two established by the work of Tsaknias and Wiese and…
We solve two conjectures of Ceken-Palmieri-Wang-Zhang concerning discriminants and give some applications.
This supplementary part of the paper gr-qc 9312038 contains the necessary proofs of the claims stated in the main part.
The usual product $m\cdot n$ on $\mathbb{Z}$ can be viewed as the sum of $n$ terms of an arithmetic progression whose first term is $a_{1}=m-n+1$ and whose difference is $d=2$. Generalizing this idea, we define new similar product mappings,…
We discuss several enumerative results for irreducible polynomials of a given degree and pairs of relatively prime polynomials of given degrees in several variables over finite fields. Two notions of degree, the {\em total degree} and the…
We prove an extension of the Thue-Vinogradov Lemma and show some applications. This paper is another example for the application of the polynomial method.
We give a new proof of Dunn's additivity for the little $n$-cubes operads $C_n$, which has the advantage of being considerably shorter than the ones in the literature. At the end we remark on how our proof can be adjusted to work for the…
Statistical distribution of the primes in an arithmetic progression is considered. The estimation of prime numbers is given and combinatorial methods are used to calculate the twin primes on the available interval. The distribution and…
In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.
Two inequalities concerning the symmetry of the zeta-function and the Ramanujan $\tau$-function are improved through the use of some elementary considerations.
In this paper we continue our study, begun in part I, of the exceptional set of integers, not restricted by elementary congruence conditions, which cannot be represented as sums of three or four squares of primes. We correct a serious…
In this short note we establish new refinements of multidimensional Szemeredi and polynomial van der Waerden theorems along the shifted primes.
In this note we improve on the results of our earlier paper[BLGG12], proving a near-optimal theorem on the existence of ordinary lifts of a mod l Hilbert modular form for any odd prime l.
Green and Tao proved that the primes contains arbitrarily long arithmetic progressions. We show that, essentially the same proof leads to the following result: The primes in an short interval contains many arithmetic progressions of any…