Results 51 to 60 of about 5,332 (130)
Normalized solutions of the critical Schrödinger–Bopp–Podolsky system with logarithmic nonlinearity
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract In this paper, we study the following critical Schrödinger–Bopp–Podolsky system driven by the p$p$‐Laplace operator and a logarithmic nonlinearity: −Δpu+V(εx)|u|p−2u+κϕu=λ|u|p−2u+ϑ|u|p−2ulog|u|p+|u|p*−2uinR3,−Δϕ+a2Δ2ϕ=4π2u2inR3.$$\begin{equation*} {\begin{cases} -\Delta _p u+\mathcal {V}(\varepsilon x)|u|^{p-2}u+\kappa \phi u=\lambda |u|^{p-2 ...
Sihua Liang +3 more
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Averaged Form of the Hardy-Littlewood Conjecture
, 2016 We study the prime pair counting functions $ _{2k}(x),$ and their averages over $2k.$ We show that good results can be achieved with relatively little effort by considering averages. We prove an asymptotic relation for longer averages of $ _{2k}(x)$ over $2k \leq x^ ,$ $ > 7/12,$ and give an almost sharp lower bound for fairly short averages ...
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Moments of the Riemann zeta function at its local extrema
Mathematika, Volume 71, Issue 4, October 2025.Abstract Conrey, Ghosh and Gonek studied the first moment of the derivative of the Riemann zeta function evaluated at the non‐trivial zeros of the zeta function, resolving a problem known as Shanks' conjecture. Conrey and Ghosh studied the second moment of the Riemann zeta function evaluated at its local extrema along the critical line to leading order.
Andrew Pearce‐Crump
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The algorithm for the $2d$ different primes and Hardy-Littlewood conjecture
, 2014 We give an estimation of the existence density for the $2d$ different primes by using a new and simple algorithm for getting the $2d$ different primes. The algorithm is a kind of the sieve method, but the remainders are the central numbers between the $2d$ different primes.
Fujimoto, Minoru, Uehara, Kunihiko
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Mathematika, Volume 71, Issue 4, October 2025.Abstract Let μ$\mu$ be a probability measure on R$\mathbb {R}$. We give conditions on the Fourier transform of its density for functionals of the form H(a)=∫Rnh(⟨a,x⟩)μn(dx)$H(a)=\int _{\mathbb {R}^n}h(\langle a,x\rangle)\mu ^n(dx)$ to be Schur monotone. As applications, we put certain known and new results under the same umbrella, given by a condition
Andreas Malliaris
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Ramanujan Cayley Graphs of the Generalized Quaternion Groups and the Hardy–Littlewood Conjecture [PDF]
, 2017 In this article, we investigate the bound of the valency of the Cayley graphs of the generalized quaternion groups which guarantees to be Ramanujan. As is the cases of the cyclic and dihedral groups in our previous studies, we show that the determination of the bound in a special setting is related to the classical Hardy-Littlewood conjecture for ...
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First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet
Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1523-1608, September 2025.Abstract For any p∈(1,∞)$p \in (1,\infty)$, we construct p$p$‐energies and the corresponding p$p$‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular ...
Mathav Murugan, Ryosuke Shimizu
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Ramanujan circulant graphs and the conjecture of Hardy-Littlewood and Bateman-Horn
, 2013 In this paper, we determine the bound of the valency of the odd circulant graph which guarantees to be a Ramanujan graph for each fixed number of vertices. In almost of the cases, the bound coincides with the trivial bound, which comes from the trivial estimate of the largest non-trivial eigenvalue of the circulant graph.
Hirano, Miki +2 more
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Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1656-1702, September 2025.Abstract Let (Mn,g)$(M^n,g)$ be a complete Riemannian manifold which is not isometric to Rn$\mathbb {R}^n$, has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature decay. We prove that there exists a set G⊂(0,∞)$\mathcal {G}\subset (0,\infty)$ with density 1 at infinity such that for every V∈G$V\in \mathcal {G}$ there ...
Gioacchino Antonelli +2 more
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Correlations of the squares of the Riemann zeta function on the critical line
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract We compute the average of a product of two shifted squares of the Riemann zeta function on the critical line with shifts up to size T3/2−ε$T^{3/2-\varepsilon }$. We give an explicit expression for such an average and derive an approximate spectral expansion for the error term similar to Motohashi's.
Valeriya Kovaleva
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