In this paper we investigate the continuity property of several invariant sets J, J⁺ and J^∗ of the Hénon map H_c,a(x,y)=(x²+c+ay,ax) as the parameters (c,a)∈C² vary. More precisely, we show that, if a sequence of parameters (c_n,a_n) converges horocyclically to (c_∗,a_∗) such that H_c∗,a∗ has a semi-parabolic fixed point and |a_∗| is sufficiently small, then the corresponding invariant sets converge to those of H_c∗,a∗. This in particular generalizes the previous result of Radu and Tanase (Trans. Amer. Math. Soc. 370(6) (2018), 3949–3996) to the case of horocyclic convergence.

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For k≥2, we let A=(a₁, a₂, . . . , a_k) be a k-tuple of positive integers with gcd(a₁, a₂, . . . , a_k)=1 and, for a non-negative integer s, the generalized Frobenius number of A, g(A; s) = g(a₁, a₂, . . . , a_k; s), the largest integer that has at most s representations in terms of a₁, a₂, . . . , a_k with non-negative integer coefficients. In this paper, we give a formula for the generalized Frobenius number of three positive integers (a₁, a₂,a₃) with certain conditions.

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In the present paper, we determine the algebraic relations among the tractable coordinates of logarithms of Anderson t-modules constructed by taking the tensor product of Drinfeld modules of rank r defined over the algebraic closure of the rational function field and their (r− 1)th exterior powers with the Carlitz tensor powers. Our results, in the case of the ten- sor powers of the Carlitz module, generalize the work of Chang and Yu [Adv. Math. 216(1) (2007), 321–345] on the algebraic independence of polylogarithms.

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Let BG be the classifying space of an algebraic group G over a subfield k of the complex numbers C. We compute a new stable birational invariant defined by Benoist and Ottem [Duke Math. J. 170 (2021), 2719–2753] as the difference of two coniveau filtrations of a smooth projective (Ekedahl) approximation X of BG×P^∞. Then we show (without and with the unramified cohomology) that in many cases X are not stable rational.

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This paper studies the harmonic means of positive functions on weighted Herz– Morrey spaces. We establish the norm inequalities for the harmonic means of positive func- tions on weighted Herz–Morrey spaces. This result is an extension of the harmonic means of positive functions on weighted Lebesgue spaces. As a special case of the main result, we have the norm inequalities of the harmonic means of positive functions on weighted Herz spaces.

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A simply connected rational CW complex X is called an F₀-space if it has finite-dimensional homotopy, finite-dimensional cohomology, and positive Euler characteristic. Making use of Whitehead’s certain exact sequence, this paper aims to study the group E(X) of self-homotopy equivalences of X and its subgroup E_*(X) constituted by elements inducing the identity on the homology groups. Specifically, we prove that E_*(X) is trivial and E(X) is isomorphic to a certain subgroup of Q^*×E(X^m-1), where m is the formal dimension of X, X^m-1 is its (m-1)-skeleton, and Q^*=Q\{0}.

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The main purpose of this paper is to introduce a new smooth version of a CW complex named a fat CW complex, and to show that it includes all closed manifolds, because existing smooth versions of CW complexes, e.g., that of Iwase (Kyushu J. Math. 76(1) (2022), 177–186), do not have such a property. We also verify that the de Rham theorem holds for a fat CW complex and that a regular CW complex is reflexive in the sense of Batubenge, Iglesias-Zemmour, Karshon, and Watts (Rocky Mountain J. Math. To appear). Further, any topological CW complex is topologically homotopy equivalent to a fat CW complex. So, a fat CW complex enjoys many nice properties.

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We give some formulas for the degree-two part of the LMO (Le–Murakami– Ohtsuki) invariant of cyclic branched covers of some genus-one knots with trivial Alexander polynomial. More concretely, we present them by using several Vassiliev invariants, where we use the 3-loop polynomial for their proofs. Furthermore, we show the existence of knots whose values of 3-loop invariant cannot be reduced. This paper is a sequel to the author’s previous paper (J. Knot Theory Ramifications 33(7) (2024), 2450023).

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