Let X be an algebraic variety over k such that X = X ⊗_k k is cellular. We study torsion elements in the Chow ring CH^∗(X) which correspond to v_iy in the algebraic cobordism Ω^∗(X) where 0 ≠y ∈CH^∗(X)/p and v_i is the generator of BP^∗with |v_i| = −2(pⁱ − 1). In particular, we try to compute CH^∗(X) from Ω^∗(X) when X are twisted complete flag varieties.

Let E_−D be the elliptic curve y² = x³ + Dx defined over K = ℚ(i) for D ∈ K which is coprime to 2. In this paper, we give a lower bound for the 2-adic valuation of the algebraic part of the central value of the Hecke L-function associated to E_−D.

We study the Berezin correspondence and the Stratonovich–Weyl correspondence associated with a holomorphic representation of the semi-direct product H ⋊ SU(p, q), where H is the (2p + 2q + 1)-dimensional Heisenberg group.

The scattering problem for the two-dimensional nonlinear Klein–Gordon equation with exponential nonlinearity 𝒩(u) is studied. It has been shown that the scattering operator 𝑺 ∶ (f₋, g₋) ↦ (f₊, g₊) is well defined on a neighborhood in the energy space ℋ ∶ = H¹(ℝ²) ⊕ L²(ℝ²) of 0. In this paper, we establish inequalities for the smoothness and decay of the output data (f₊, g₊) dependent on the smoothness and decay of the input data (f₋, g₋) and the smoothness of 𝒩. The inequalities imply that (f₊, g₊) belongs to the Schwartz space 𝒮(ℝ²) ⊕ 𝒮(ℝ²) if (f₋,g₋) is in 𝒮(ℝ²) ⊕ 𝒮(ℝ²) and small in the sense of ℋ, and that we have a simple sufficient condition for (f₋, g₋) and 𝒩such that all order partial derivatives of f₊ and g₊ decay more rapidly than a similar exponential function.

In this article we construct infinitely many new families of non-congruent numbers,each containing infinitely many non-congruent numbers with arbitrarily many triples of prime factors.

We clarify the Lie algebra structure of the contiguity relations for Lauricella’s hypergeometric functions (HGFs) of n independent variables F_A and F_B from the point of view of Gelfand’s HGF on the Grassmannian. The key point is to identify F_A and F_B as the restriction of Gelfand’s HGF to some specific stratum of dimension n of the Grassmannian, and to relate the contiguity operators to the root vectors in the root decomposition of the Lie algebra of the general linear group whose one-parameter subgroup acts on the Grassmannian and preserves the specific stratum. We give the explicit forms of the contiguity relations and contiguity operators for F_A and F_B.

This paper is devoted to the regularity of generalized random spectral measures. It consists of two main results as well as some applications. Firstly, we prove that every generalized random spectral measure defined on a locally compact metric space with values in a separable Hilbert space is regular. A solution of the Schrödinger-type random equation is obtained as an application. Secondly, we show that every finitely additive generalized random spectral measure defined on an arbitrary measurable space with values in a finite-dimensional Hilbert space is also regular. As an application, a random version of Jordan’s classical decomposition theorem for a matrix is provided.

In this paper, we study the asymptotic behavior of the counting function of composite numbers with three constrained prime factors. Our constraint is that the largest prime factor is bounded above by a general increasing function with respect to either the smallest or the second smallest prime factor.

The Aronson–Bénilan gradient estimate for the porous medium equation has been studied as a counterpart to the Li–Yau gradient estimate for the heat equation. In this paper, we give the Aronson–Bénilan gradient estimates for the porous medium equation on weighted Riemannian manifolds under lower bounds of N-weighted Ricci curvature with 𝜀-range for some N < 0. This is a generalization of those estimates under constant lower N-weighted Ricci curvature bounds with N ∈ [n,∞).

In this paper, we will show the existence of non-holomorphic hyperelliptic minimal surfaces of genus four in flat 4-tori. Moreover, we compute two kinds of geometric invariants of such minimal surfaces, namely, the Morse index and the signature. This work treats the higher-genus and -codimension case of the previous papers, and the situation is quite different. We solve the difficulty by the Micallef–Wolfson technique. As its application, we obtain the existence of non-holomorphic hyperelliptically stable minimal surfaces of genus four in flat 4-tori.

In this paper we study the Möbius disjointness property for infinite measure-preserving systems. We show that, for ergodic infinite measure-preserving transformations, the disjointness property does not hold at almost all points in the class of continuous, bounded, and integrable observables. Next, we show that, for periodic, continuous observables, the disjointness property holds true for a large class of infinite measure-preserving rank-one systems.