Add to ORKGWe relate the size of the error term in the Hardy-Littlewood conjectured formula for the number of prime pairs to the $L^{1}$ norm of an exponential sum over the primes formed with the von Mangoldt function.Comment: 21 pages, 3 figures, and 1 tabl
This article determines a lower bound for the number of twin primes $p$ and $p+2$ up to a large numb...
summary:In this note, we show that the counting function of the number of composite positive integer...
The Hardy-Littlewood prime k-tuples conjecture[18,29,34] and Erdos-Turan conjecture(every set of int...
AbstractBy (extended) Wiener–Ikehara theory, the prime-pair conjectures are equivalent to simple pol...
AbstractWe study, under the assumption of the Generalized Riemann Hypothesis, the individual and mea...
We provide an explicit $O(x/T)$ error term for the Riemann--von Mangoldt formula by making results o...
This short note provides a sharper upper bound of a well known inequality for the sum of divisors fu...
Taking $r>0$, let $\pi_{2r}(x)$ denote the number of prime pairs $(p,\,p+2r)$ with $p\le x$. The pri...
The sequence 3,5,9,11,15,19,21,25,29,35,… consists of odd legs in right triangles with integer si...
Let $1<c<d$ be two relatively prime integers and $g_{c,d}=cd-c-d$. We confirm, by employing the Hard...
We prove that the primes below $x$ are, on average, equidistributed in arithmetic progressions to sm...
We prove an explicit error term for the psi(x, chi) function assuming the Generalized Riemann Hypoth...
We prove an explicit error term for the psi(x, chi) function assuming the Generalized Riemann Hypoth...
In 2020, Roger Baker \cite{Bak} proved a result on the exceptional set of moduli in the prime number...
summary:In this note, we show that the counting function of the number of composite positive integer...
This article determines a lower bound for the number of twin primes $p$ and $p+2$ up to a large numb...
summary:In this note, we show that the counting function of the number of composite positive integer...
The Hardy-Littlewood prime k-tuples conjecture[18,29,34] and Erdos-Turan conjecture(every set of int...
AbstractBy (extended) Wiener–Ikehara theory, the prime-pair conjectures are equivalent to simple pol...
AbstractWe study, under the assumption of the Generalized Riemann Hypothesis, the individual and mea...
We provide an explicit $O(x/T)$ error term for the Riemann--von Mangoldt formula by making results o...
This short note provides a sharper upper bound of a well known inequality for the sum of divisors fu...
Taking $r>0$, let $\pi_{2r}(x)$ denote the number of prime pairs $(p,\,p+2r)$ with $p\le x$. The pri...
The sequence 3,5,9,11,15,19,21,25,29,35,… consists of odd legs in right triangles with integer si...
Let $1<c<d$ be two relatively prime integers and $g_{c,d}=cd-c-d$. We confirm, by employing the Hard...
We prove that the primes below $x$ are, on average, equidistributed in arithmetic progressions to sm...
We prove an explicit error term for the psi(x, chi) function assuming the Generalized Riemann Hypoth...
We prove an explicit error term for the psi(x, chi) function assuming the Generalized Riemann Hypoth...
In 2020, Roger Baker \cite{Bak} proved a result on the exceptional set of moduli in the prime number...
summary:In this note, we show that the counting function of the number of composite positive integer...
This article determines a lower bound for the number of twin primes $p$ and $p+2$ up to a large numb...
summary:In this note, we show that the counting function of the number of composite positive integer...
The Hardy-Littlewood prime k-tuples conjecture[18,29,34] and Erdos-Turan conjecture(every set of int...