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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：First-order factors of linear Mahler operators
线性 Mahler operators 一阶因子
2023/4/27
We develop and compare two algorithms for computing first-order right-hand factors in the ring of linear Mahler operators l_r M^r+?+l_1 M+l_0 where l_0,…,l_r are polynomials in x and Mx=x^b M for some...
Linear Mahler Measures and Double L-values of Modular Forms
Linear Mahler Measures Double L-values of Modular Forms Number Theory
2012/6/27
We consider the Mahler measure of the polynomial 1+x_1+x_2+x_3+x_4, which is the first case not yet evaluated explicitly. A conjecture due to F. Rodriguez-Villegas represents this Mahler measure as a ...
From $L$-series of elliptic curves to Mahler measures
Mahler measure L-value of elliptic curve hypergeometric series
2011/1/21
We prove the conjectural relations between Mahler measures and L-values of elliptic curves of conductors 20 and 24. We also present new hyper-geometric expressions for L-values of CM elliptic curves o...
Let K be a convex body in Rn with Santal´o point at 0. We show that if K has a point on the boundary with positive generalized Gauß curvature, then the volume product |K||K◦| is not ...
Algebraic Independence of Certain Generalized Mahler Type Numbers
Mahler type numbers Generalized Mahler type numbers Algebraic independence Multiplicative dependence
2007/12/11
In this paper the generalized Mahler type number $M_h(g;A,T)$ is defined, and in the case of multiplicatively dependent parameters $g_i, h_i (1 \leq i \leq s)$ the algebraic independence of the number...
On a Problem of Mahler Concerning the Approximation of Exponentials and Logarithms
Mahler Concerning Approximation of Exponentials Logarithms
2010/11/1
We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.
Hans Rott (1858-1884) -- the missing link between Bruckner and Mahler
Bruckner Mahler Vienna Rott Brahms string quartet Richter symphony
2010/3/29
The relationship between Gustav Mahler and his friend/significant influence Hans Rott is discussed in this essay, as well as the relationship of Bruckner and his favourite student Rott. The essay cont...