Journal of the London Mathematical Society-Second Series最新文献

We first develop some criteria for a general divisor to be strongly Euler-homogeneous in terms of the Fitting ideals of certain modules. We also study new variants of Saito-holonomicity, generalizing Koszul-free–type properties and characterizing them in terms of the same Fitting ideals. Thanks to these advances, we are able to make progress in the understanding of a conjecture from 2002: A free divisor satisfying the Logarithmic Comparison Theorem (LCT) must be strongly Euler-homogeneous. Previously, it was known to be true only for ambient dimension $��n�⩽�3�$ or assuming Koszul-freeness. We prove it in the following new cases: assuming strong Euler-homogeneity outside a discrete set of points; assuming the divisor is weakly Koszul-free; for $��n�=�4�$; for linear free divisors in $��n�=�5�$. Finally, we refute a conjecture stating that all linear free divisors satisfy LCT, are strongly Euler-homogeneous and have $�b$-functions with symmetric roots about $��-�1�$.

In this paper, we investigate the validity of a quantitative version of stability for the critical Hardy–Hénon equation

Total positivity of matrices plays an important role in various branches of mathematics. In this paper, we present some criteria for the coefficientwise total positivity of Riordan arrays and the coefficientwise Hankel-total positivity of the row-generating polynomial sequence of Riordan arrays. In addition, we also give some criteria for the coefficientwise Hankel-total positivity of sequences of coefficients of compositional functions and some results for triangular convolutions preserving Stieltjes moment properties. As applications, we first obtain the coefficientwise Hankel-total positivity of two kinds of multivariate Fuss–Narayana–Riordan polynomials, which implies those of two kinds of multivariate Fuss–Narayana polynomials proved by Pétréolle, Sokal and Zhu (Mem. Amer. Math. Soc., 2023). Then, we also derive the total positivity of Fuss–Catalan Riordan arrays, unifying total positivity results of a few well-known combinatorial triangles.

We study the distortion of intermediate dimension under supercritical Sobolev mappings and also under quasiconformal or quasisymmetric homeomorphisms. In particular, we extend to the setting of intermediate dimensions both the Gehring–Väisälä theorem on dilatation-dependent quasiconformal distortion of dimension and Kovalev's theorem on the nonexistence of metric spaces with conformal dimension strictly between zero and one. Applications include new contributions to the quasiconformal classification of Euclidean sets and a new sufficient condition for the vanishing of conformal box-counting dimension. We illustrate our conclusions with specific consequences for Bedford–McMullen carpets, samples of Mandelbrot percolation, and product sets containing a polynomially convergent sequence factor.

We prove Pólya's conjecture for the eigenvalues of the Dirichlet Laplacian on annular domains. Our approach builds upon and extends the methods we previously developed for disks and balls. It combines variational bounds, estimates of Bessel phase functions, refined lattice point counting techniques and a rigorous computer-assisted analysis. As a by-product, we also derive a two-term upper bound for the Dirichlet eigenvalue counting function of the disk, improving upon Pólya's original estimate.

The main goal of this paper is to establish the higher dimensional Nevanlinna theory in tropical geometry. We first develop a theory of tropical meromorphic functions (tropical holomorphic maps) in several real variables, such as the proximity function, counting function and characteristic function, the first main theorem, higher dimensional tropical versions of the logarithmic derivative lemmas. Based on this, for algebraically non-degenerate tropical holomorphic maps $�f$ with subnormal growth from $�R^n$ into tropical projective space $�{\mathrm{TP}}^m$ intersecting tropical hypersurfaces $�{�\left\{�V_{P_j}�\right\}�}_{�j�=�1�}^q$ with degree $�d_j$, we then obtain the second main theorem

Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no analogues in the literature and rely on a new technique. The results are especially transparent for self-adjoint operators.

We revisit certain one-parameter families of affine covers arising naturally from Euler's integral representation of hypergeometric functions. We introduce a partial compactification of this family. We show that the zeta function of the fibers in the family can be written as an explicit product of $�L$-series attached to nondegenerate hypergeometric motives and zeta functions of tori, twisted by Hecke Grössencharacters. This permits a combinatorial algorithm for computing the Hodge numbers of the family.

We study the weighted constant scalar curvature Kähler equations on mildly singular Kähler varieties. Assuming the existence of a suitable resolution of singularities, we establish the existence of singular weighted cscK metrics when the weighted Mabuchi functional is coercive for an extremal weight. This extends the works of Chen–Cheng and He to the singular weighted setting. Moreover, we provide a method for constructing examples of singular cscK metrics inspired by the work of Arezzo–Pacard. In contrast to the usual gluing techniques, our approach does not require a precise understanding about of the metric behavior near the singular locus.