Assuming the Riemann Hypothesis we prove that the interval [N, N + H] contains an integer which is a sum of a prime and two squares of primes provided that H ≥ C(log N)4, where C > 0 is an effective constant
Abstract. For any > 0 and any non-exceptional modulus q ≥ 3, we prove that, for x large enough (x...
yesSuppose that the Riemann hypothesis holds. Suppose that ψ₁(x) = ∑ Λ(n), n≤x {(1/2)n¹/ᶜ}N½⁺¹⁰ᵋ, ε ...
Assume the Riemann Hypothesis and a weaker form of Montgomery's pair correlation conjecture, i.e...
Assuming the Riemann Hypothesis we prove that the interval $[N,N+H]$ contains an integer which ...
AbstractIn this paper, we are able to sharpen Hua's classical result by showing that each sufficient...
We prove that suitable asymptotic formulae in short intervals hold for the problems of representing ...
Let $X$ be a large parameter. We will first give a new estimate for the integral moments of primes ...
International audienceLet Λ(n) be the von Mangoldt function, x real and 2 ≤ y ≤ x. This paper improv...
We prove that suitable asymptotic formulae in short intervals hold for the problems of representing ...
Under the assumption of the Riemann Hypothesis (RH), we prove explicit quantitative relations betwe...
We prove the analog of Cramer's short intervals theorem for primes in arithmetic progressions and pr...
AbstractAssuming that the Generalized Riemann Hypothesis (GRH) holds, we prove an explicit formula f...
Let k 651 be an integer. We prove that a suitable asymptotic formula for the average number of repre...
Abstract. The set of short intervals between consecutive primes squared has the pleasant—but seeming...
In this paper, on the assumption of the Riemann hypothesis, we give explicit upper bounds on the dif...
Abstract. For any > 0 and any non-exceptional modulus q ≥ 3, we prove that, for x large enough (x...
yesSuppose that the Riemann hypothesis holds. Suppose that ψ₁(x) = ∑ Λ(n), n≤x {(1/2)n¹/ᶜ}N½⁺¹⁰ᵋ, ε ...
Assume the Riemann Hypothesis and a weaker form of Montgomery's pair correlation conjecture, i.e...
Assuming the Riemann Hypothesis we prove that the interval $[N,N+H]$ contains an integer which ...
AbstractIn this paper, we are able to sharpen Hua's classical result by showing that each sufficient...
We prove that suitable asymptotic formulae in short intervals hold for the problems of representing ...
Let $X$ be a large parameter. We will first give a new estimate for the integral moments of primes ...
International audienceLet Λ(n) be the von Mangoldt function, x real and 2 ≤ y ≤ x. This paper improv...
We prove that suitable asymptotic formulae in short intervals hold for the problems of representing ...
Under the assumption of the Riemann Hypothesis (RH), we prove explicit quantitative relations betwe...
We prove the analog of Cramer's short intervals theorem for primes in arithmetic progressions and pr...
AbstractAssuming that the Generalized Riemann Hypothesis (GRH) holds, we prove an explicit formula f...
Let k 651 be an integer. We prove that a suitable asymptotic formula for the average number of repre...
Abstract. The set of short intervals between consecutive primes squared has the pleasant—but seeming...
In this paper, on the assumption of the Riemann hypothesis, we give explicit upper bounds on the dif...
Abstract. For any > 0 and any non-exceptional modulus q ≥ 3, we prove that, for x large enough (x...
yesSuppose that the Riemann hypothesis holds. Suppose that ψ₁(x) = ∑ Λ(n), n≤x {(1/2)n¹/ᶜ}N½⁺¹⁰ᵋ, ε ...
Assume the Riemann Hypothesis and a weaker form of Montgomery's pair correlation conjecture, i.e...
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