LAUSR

Hausdorff and packing dimensions and measures for nonlinear transversally non-conformal thin solenoids

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0 Published in 2021 at "Ergodic Theory and Dynamical Systems"

DOI: 10.1017/etds.2021.94

Abstract: We extend the results of Hasselblatt and Schmeling [Dimension product structure of hyperbolic sets. Modern Dynamical Systems and Applications. Eds. B. Hasselblatt, M. Brin and Y. Pesin. Cambridge University Press, New York, 2004, pp. 331–345]… read more here.

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Subshifts and colorings on ascending HNN-extensions of finitely generated abelian groups

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0 Published in 2021 at "Ergodic Theory and Dynamical Systems"

DOI: 10.1017/etds.2021.95

Abstract: For an ascending HNN-extension $G*_{\psi }$ of a finitely generated abelian group G, we study how a synchronization between the geometry of the group and weak periodicity of a configuration in $\mathcal {A}^{G*_{\psi }}$ forces… read more here.

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Global rigidity of higher rank lattice actions with dominated splitting

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2 Published in 2023 at "Ergodic Theory and Dynamical Systems"

DOI: 10.1017/etds.2023.31

Abstract: Let $\alpha $ be a $C^{\infty }$ volume-preserving action on a closed n-manifold M by a lattice $\Gamma $ in $\mathrm {SL}(n,\mathbb {R})$ , $n\ge 3$ . Assume that there is an element $\gamma \in… read more here.

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K-STABLE DIVISORS IN OF DEGREE

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1 Published in 2023 at "Nagoya Mathematical Journal"

DOI: 10.1017/nmj.2023.5

Abstract: We prove that every smooth divisor in $\mathbb {P}^1\times \mathbb {P}^1\times \mathbb {P}^2$ of degree $(1,1,2)$ is K-stable. read more here.

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OVERPARTITIONS RELATED TO THE MOCK THETA FUNCTION

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0 Published in 2020 at "Bulletin of The Australian Mathematical Society"

DOI: 10.1017/s0004972719001618

Abstract: Recently, Brietzke, Silva and Sellers [‘Congruences related to an eighth order mock theta function of Gordon and McIntosh’, J. Math. Anal. Appl.479 (2019), 62–89] studied the number $v_{0}(n)$ of overpartitions of $n$ into odd parts without… read more here.

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COMPUTING POINTS ON BIELLIPTIC MODULAR CURVES OVER FIXED QUADRATIC FIELDS

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1 Published in 2023 at "Bulletin of the Australian Mathematical Society"

DOI: 10.1017/s0004972723000333

Abstract: We present a Mordell–Weil sieve that can be used to compute points on certain bielliptic modular curves $X_0(N)$ over fixed quadratic fields. We study $X_0(N)(\mathbb {Q}(\sqrt {d}))$ for $N \in \{ 53,61,65,79,83,89,101,131 \}$ and ${\lvert… read more here.

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ON THE ITERATES OF THE SHIFTED EULER’S FUNCTION

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1 Published in 2023 at "Bulletin of the Australian Mathematical Society"

DOI: 10.1017/s0004972723000394

Abstract: Let $\varphi $ be Euler’s function and fix an integer $k\ge 0$ . We show that for every initial value $x_1\ge 1$ , the sequence of positive integers $(x_n)_{n\ge 1}$ defined by $x_{n+1}=\varphi (x_n)+k$ for… read more here.

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DIOPHANTINE EQUATIONS OF THE FORM OVER FUNCTION FIELDS

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1 Published in 2023 at "Bulletin of the Australian Mathematical Society"

DOI: 10.1017/s0004972723000412

Abstract: Let $\ell $ and p be (not necessarily distinct) prime numbers and F be a global function field of characteristic $\ell $ with field of constants $\kappa $ . Assume that there exists a prime… read more here.

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THE -SCHUR ALGEBRAS AND -SCHUR DUALITIES OF FINITE TYPE

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0 Published in 2020 at "Journal of The Institute of Mathematics of Jussieu"

DOI: 10.1017/s1474748020000031

Abstract: We formulate a $q$ -Schur algebra associated with an arbitrary $W$ -invariant finite set $X_{\text{f}}$ of integral weights for a complex simple Lie algebra with Weyl group $W$ . We establish a $q$ -Schur duality… read more here.

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THÉORIE DE BRUHAT-TITS POUR LES GROUPES QUASI-RÉDUCTIFS

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0 Published in 2021 at "Journal of The Institute of Mathematics of Jussieu"

DOI: 10.1017/s1474748020000572

Abstract: Soient K un corps discrètement valué et hensélien, ${\mathcal {O}}$ son anneau d'entiers supposé excellent, $\kappa $ son corps résiduel supposé parfait et G un K-groupe quasi-réductif, c'est-à-dire lisse, affine, connexe et à radical unipotent… read more here.

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ON FUNDAMENTAL FOURIER COEFFICIENTS OF SIEGEL CUSP FORMS OF DEGREE 2

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0 Published in 2021 at "Journal of the Institute of Mathematics of Jussieu"

DOI: 10.1017/s1474748021000542

Abstract: Let F be a Siegel cusp form of degree $2$ , even weight $k \ge 2$ , and odd square-free level N. We undertake a detailed study of the analytic properties of Fourier coefficients $a(F,S)$… read more here.

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