Zobrazeno 1 - 10
of 20 288
pro vyhledávání: '"P Mahler"'
Autor:
Rajchert, Andrew
We explore Mahler numbers originating from functions $f(z)$ that satisfy the functional equation $f(z) = (A(z)f(z^d) + C(z))/B(z)$. A procedure to compute the irrationality exponents of such numbers is developed using continued fractions for formal L
Externí odkaz:
http://arxiv.org/abs/2411.10733
Autor:
Mastrantonis, Vlassis
$L^p$-polarity and $L^p$-Mahler volumes were recently introduced by Berndtsson, Rubinstein, and the author as a new approach, inspired by complex geometry, to the Mahler, Bourgain, and Blocki conjectures. This paper serves two purposes. First, it int
Externí odkaz:
http://arxiv.org/abs/2411.10439
Autor:
Samart, Detchat, Tao, Zhengyu
We consider Mahler measures of two well-studied families of bivariate polynomials, namely $P_t=x+x^{-1}+y+y^{-1}+\sqrt{t}$ and $Q_t=x^3+y^3+1-\sqrt[3]{t}xy$, where $t$ is a complex parameter. In the cases when the zero loci of these polynomials defin
Externí odkaz:
http://arxiv.org/abs/2409.14714
Autor:
Katagiri, Yu
Kurokawa, Lal\'{\i}n and Ochiai introduced and studied the higher Mahler measures, which are generalization of the classical Mahler measure. In this article, we introduce $p$-adic higher Mahler measures and prove $p$-adic analogues of Akatsuka's resu
Externí odkaz:
http://arxiv.org/abs/2408.05724
Autor:
Viswanathan, Gandhimohan M.
This work establishes links between the Ising model and elliptic curves via Mahler measures. First, we reformulate the partition function of the Ising model on the square, triangular and honeycomb lattices in terms of the Mahler measure of a Laurent
Externí odkaz:
http://arxiv.org/abs/2407.19531
Autor:
Carton, Olivier, Yassawi, Reem
We define generalised equations of Z-Mahler type, based on the Zeckendorf numeration system. We show that if a sequence over a commutative ring is Z-regular, then it is the sequence of coefficients of a series which is a solution of a Z-Mahler equati
Externí odkaz:
http://arxiv.org/abs/2405.01953
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Akademický článek
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We develop and compare two algorithms for computing first-order right-hand factors in the ring of linear Mahler operators$\ell_r M^r + \dots + \ell_1 M + \ell_0$where $\ell_0, \dots, \ell_r$ are polynomials in~$x$ and $Mx = x^b M$ for some integer $b
Externí odkaz:
http://arxiv.org/abs/2403.11545
Autor:
Wang, Weijia, Zhang, Hao
We introduce the quaternionic Mahler measure for non-commutative polynomials, extending the classical complex Mahler measure. We establish the existence of quaternionic Mahler measure for slice regular polynomials in one and two variables. We study t
Externí odkaz:
http://arxiv.org/abs/2403.02851