Steklov Mathematical Institute

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most citedQuantum Inverse Scattering Method and Correlation Functions

866 citations

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Showing 2014 · math.NTShow all

8 papers · 2 filters

math.NT2014★ 13 cited

Long gaps between primes

Kevin Ford, Ben Green, Sergei Konyagin +2

Let $p_{n}$ denotes the $n$ -th prime. We prove that $p_{n + 1} \leq X max (p_{n + 1} - p_{n}) ≫ \frac{lo g X lo g lo g X lo g lo g lo g lo g X}{lo g lo g lo g X}$ for sufficiently large $…

math.NT2014

Yet another representation for the sum of reciprocals of the nontrivial zeros of the Riemann zeta-function

Yuri Matiyasevich

The positivity of the sum from the title is the first condition in the well-known criterium for the validity of the Riemann Hypothesis suggested by X.-J. Li. In the paper this valu…

math.NT2014

Distribution of complex algebraic numbers

Friedrich Götze, Dzianis Kaliada, Dmitry Zaporozhets

For a region $Ω \subset C$ denote by $Ψ (Q; Ω)$ the number of complex algebraic numbers in $Ω$ of degree $\leq n$ and naive height $\leq Q$ . We show that $$ Ψ(Q;Ω)=\frac{Q^{n+…

math.NT2014★ 16 cited

Large gaps between consecutive prime numbers

Kevin Ford, Ben Green, Sergei Konyagin +1

Let $G (X)$ denote the size of the largest gap between consecutive primes below $X$ . Answering a question of Erdos, we show that $$G(X) \geq f(X) \frac{\log X \log \log X \log \log…

math.NT2014★ 4 cited

Discriminant and root separation of integral polynomials

Friedrich Götze, Dmitry Zaporozhets

Consider a random polynomial $G_{Q} (x) = ξ_{Q, n} x^{n} + ξ_{Q, n - 1} x^{n - 1} + ... + ξ_{Q, 0}$ with independent coefficients uniformly distributed on $2 Q + 1$ integer points ${- Q, ..., Q}$ . Den…

math.NT2014★ 8 cited

On the large values of the Riemann zeta-function on short segments of the critical line

M. A. Korolev

In this paper, we obtain a series of new conditional lower bounds for the modulus and the argument of the Riemann zeta function on very short segments of the critical line, based o…