相关论文: Primes in Quadratic Progressions on Average

In this paper, we prove a theorem on the distribution of primes in cubic progressions on average.

In this paper, we establish some theorems on the distribution of primes in higher-order progressions on average.

We verify the Hardy-Littlewood conjecture on primes in quadratic progressions on average. The results in the present paper significantly improve those of a previous paper of the authors(arXiv:math.NT/0605563).

This is a survey article on the Hardy-Littlewood conjecture about primes in quadratic progressions. We recount the history and quote some results approximating this hitherto unresolved conjecture.

We obtain an upper bound for the distribution of primes in the form $n^4 + k$ up to $x$, averaged over $k$ with small square-full part. As a corollary, we show that for almost all $k$, there is an expected amount of primes in the form $n^4…

We develop a theory of multiplicative functions (with values inside or on the unit circle) in arithmetic progressions analogous to the well-known theory of primes in arithmetic progressions.

In this paper, we will give some estimation for the average error of the prime number theorem.

We prove explicit versions of Cram\'er's theorem for primes in arithmetic progressions, on the assumption of the generalized Riemann hypothesis.

The pentagonal number theorem is extended to the sequence of the number of integer partitions with all parts equal. The new pentagonal number theorem implies that the distribution of the primes is just a specific detail of the application…

Let $D$ be a square-free integer. Under certain conditions on $D$, we characterize non-constant arithmetic progressions of squares over quadratic extensions of $\mathbb{Q}(\sqrt{D})$.

Building on the concept of pretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.

We investigate the problem of the distribution of sums of functions of prime numbers located on an arithmetic progression. This problem is closely related to the problem of the distribution of prime numbers on an arithmetic progression.…

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

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 investigate the average distribution of primes represented by positive definite integral binary quadratic forms, the average being taken over negative fundamental discriminants in long ranges. In particular, we prove corresponding…

We prove the analog of Cram\'er's short intervals theorem for primes in arithmetic progressions and prime ideals, under the relevant Riemann Hypothesis. Both results are uniform in the data of the underlying structure. Our approach is based…

In our paper, we apply additive-combinatorial methods to study the distribution of the set of squares $\mathcal{R}$ in the prime field. We obtain the best upper bound on the number of gaps in $\mathcal{R}$ at the moment and generalize this…

In this paper, we prove certain theorems about three consecutive primes.

The aim of this paper is to prove Cotlar's ergodic theorem modeled on the set of primes.

We find a lower bound for the number of Chen primes in the arithmetic progression $a \bmod q$, where $(a,q)=(a+2,q)=1$. Our estimate is uniform for $q \leq \log^M x$, where $M>0$ is fixed.