Add to ORKGLet $X$ be a sufficiently large positive integer. We prove that one may choose a subset $S$ of primes with cardinality $O(\log X)$, such that a positive proportion of integers less than $X$ can be represented by $x^2 + p y^2$ for at least one of $p \in S$.Comment: 13 page
In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers l...
AbstractThe number defined by the title is denoted by Ψ(x, y). Let u = log xlog y and let ϱ(u) be th...
It is shown that every sufficiently large even integer is a sum of two primes and exactly 13 powers ...
The number of solutions to $a^2+b^2=c^2+d^2 \le x$ in integers is a well-known result, while if one ...
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number...
AbstractWe prove that the density of integers ≡2 (mod24), which can be represented as the sum of two...
We prove that the density of integers ≡2 (mod 24), which can be represented as the sum of two square...
Benford's Law describes the prevalence of small numbers as the leading digits of numbers in many set...
In 2020, Roger Baker \cite{Bak} proved a result on the exceptional set of moduli in the prime number...
Let $(\mathcal{A}_i)_{i \in [s]}$ be a sequence of dense subsets of the Boolean cube $\{0,1\}^n$ and...
If $a>b$ and $n>1$ are positive integers and $a$ and $b$ are relatively prime integers, then a large...
AbstractSuppose g is a fixed positive integer. For N⩾2, a set A⊂Z∩[1,N] is called a B2[g] set if eve...
summary:A classical result in number theory is Dirichlet's theorem on the density of primes in an ar...
AbstractErdős and Sárkőzy proposed the problem of determining the maximal density attainable by a se...
We show that in any two-coloring of the positive integers there is a color for which the set of posi...
In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers l...
AbstractThe number defined by the title is denoted by Ψ(x, y). Let u = log xlog y and let ϱ(u) be th...
It is shown that every sufficiently large even integer is a sum of two primes and exactly 13 powers ...
The number of solutions to $a^2+b^2=c^2+d^2 \le x$ in integers is a well-known result, while if one ...
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number...
AbstractWe prove that the density of integers ≡2 (mod24), which can be represented as the sum of two...
We prove that the density of integers ≡2 (mod 24), which can be represented as the sum of two square...
Benford's Law describes the prevalence of small numbers as the leading digits of numbers in many set...
In 2020, Roger Baker \cite{Bak} proved a result on the exceptional set of moduli in the prime number...
Let $(\mathcal{A}_i)_{i \in [s]}$ be a sequence of dense subsets of the Boolean cube $\{0,1\}^n$ and...
If $a>b$ and $n>1$ are positive integers and $a$ and $b$ are relatively prime integers, then a large...
AbstractSuppose g is a fixed positive integer. For N⩾2, a set A⊂Z∩[1,N] is called a B2[g] set if eve...
summary:A classical result in number theory is Dirichlet's theorem on the density of primes in an ar...
AbstractErdős and Sárkőzy proposed the problem of determining the maximal density attainable by a se...
We show that in any two-coloring of the positive integers there is a color for which the set of posi...
In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers l...
AbstractThe number defined by the title is denoted by Ψ(x, y). Let u = log xlog y and let ϱ(u) be th...
It is shown that every sufficiently large even integer is a sum of two primes and exactly 13 powers ...