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Zhonghua Li

Publications and source records attributed to Zhonghua Li.

52 records · Page 3Linked to original sources
arXiv2019

Some relations deduced from regularized double shuffle relations of multiple zeta values

It is conjectured that the regularized double shuffle relations give all algebraic relations among the multiple zeta values, and hence all other algebraic relations should be deduced from the regularized double shuffle relations. In this paper, we provide as many as the relations which can be derived from the regularized double shuffle relations, for example, the weighted sum formula of L. Guo and B. Xie, some evaluation formulas with even arguments and the restricted sum formulas of M. E. Hoffman and their generalizations.

math.NT↗
arXiv2019

Algebraic relations of interpolated multiple zeta values

Interpolated multiple zeta values can be regarded as interpolation polynomials of multiple zeta values and multiple zeta-star values. In this paper, we give some algebraic relations of interpolated multiple zeta values, such as the symmetric sum formula, the shuffle regularized sum formula, a weighted sum formula and some evaluation formulas with even arguments. All the algebraic relations provided in this paper are deduced from the extended double shuffle relations.

math.NT↗
arXiv2019

Sum of interpolated finite multiple harmonic $q$-series

We define and study the interpolated finite multiple harmonic $q$-series. A generating function of the sums of the interpolated finite multiple harmonic $q$-series with fixed weight, depth and $i$-height is computed. Some Ohno-Zagier type relation with corollaries and some evaluation formulas of the interpolated finite multiple harmonic $q$-series at roots of unity are given.

math.NT↗
arXiv2018

Weighted sum formulas of multiple zeta values with even arguments

We obtain a weighted sum formula of the zeta values at even arguments, and a weighted sum formula of the multiple zeta values with even arguments and its zeta-star analogue. The weight coefficients are given by (symmetric) polynomials of the arguments. These weighted sum formulas for the zeta values and for the multiple zeta values were conjectured by L. Guo, P. Lei and J. Zhao.

math.NT↗
arXiv2017

On q-analogues of quadratic Euler sums

In this paper we define the generalized q-analogues of Euler sums and present a new family of identities for q-analogues of Euler sums by using the method of Jackson q-integral rep- resentations of series. We then apply it to obtain a family of identities relating quadratic Euler sums to linear sums and q-polylogarithms. Furthermore, we also use certain stuffle products to evaluate several q-series with q-harmonic numbers. Some interesting new results and illustrative examples are considered. Finally, we can obtain some explicit relations for the classical Euler sums when q approaches to 1.

math.NT↗
arXiv2017

Sum of interpolated multiple $q$-zeta values

Interpolated multiple $q$-zeta values are deformation of multiple $q$-zeta values with one parameter, $t$, and restore classical multiple zeta values as $t = 0$ and $q \to 1$. In this paper, we discuss generating functions for sum of interpolated multiple $q$-zeta values with fixed weight, depth and $i$-height. The functions are systematically expressed in terms of the basic hypergeometric functions. Compared with the result of Ohno and Zagier, our result includes three generalizations: general height, $q$-deformation and $t$-interpolation. As an application, we prove some expected relations for interpolated multiple $q$-zeta values including sum formulas.

math.NT↗
arXiv2017

Stuffle product formulas of multiple zeta values

We obtain recursive formulas for the stuffle product of multiple zeta values and of multiple zeta-star values. Then we apply the formulas to prove several stuffle product formulas with one or two strings of $z_p$'s. We also describe how to use our formulas in general cases.

math.NT↗
arXiv2017

AdS Black Hole with Phantom Scalar Field

In this paper, we present an AdS black hole solution with Ricci flat horizon in Einstein-phantom scalar theory. The phantom scalar fields just depend on the transverse coordinates $x$ and $y$, and which are parameterized by the parameter $α$. We study the thermodynamics of the AdS phantom black hole. Although its horizon is a Ricci flat Euclidean space, we find that the thermodynamical properties of the black hole solution are qualitatively same as those of AdS Schwarzschild black hole. Namely there exists a minimal temperature, the large black hole is thermodynamically stable , while the smaller one is unstable, so there is a so-called Hawking-Page phase transition between the large black hole and the thermal gas solution in the AdS spacetime in Poincare coordinates. We also calculate the entanglement entropy for a strip geometry dual to the AdS phantom black holes and find that the behavior of the entanglement entropy is qualitatively the same as that of the black hole thermodynamical entropy.

hep-th↗
arXiv2017

Some relations of interpolated multiple zeta values

In this paper, the extended double shuffle relations for interpolated multiple zeta values are established. As an application, Hoffman's relations for interpolated multiple zeta values are proved. Furthermore, a generating function for sums of interpolated multiple zeta values of fixed weight, depth and height is represented by hypergeometric functions, and we discuss some special cases.

math.NT↗
arXiv2016

Shuffle product formulas of multiple zeta values

Using the combinatorial description of shuffle product, we prove or reformulate several shuffle product formulas of multiple zeta values, including a general formula of the shuffle product of two multiple zeta values, some restricted shuffle product formulas of the product of two multiple zeta values, and a restricted shuffle product formula of the product of $n$ multiple zeta values.

math.NT↗
arXiv2014

Remarks on remnants by fermions' tunnelling from black strings

Hawking's calculation is unable to predict the final stage of the black hole evaporation. When effects of quantum gravity are taken into account, there is a minimal observable length. In this paper, we investigate fermions' tunnelling from the charged and rotating black strings. With the influence of the generalized uncertainty principle, the Hawking temperatures are not only determined by the rings, but also affected by the quantum numbers of the emitted fermions. Quantum gravity corrections slow down the increases of the temperatures, which naturally leads to remnants left in the evaporation.

hep-th↗
arXiv2013

Mechanical properties of hydrogen functionalized graphene allotropes

Molecular dynamics (MD) simulations have been performed to investigate the mechanical properties of hydrogen functionalized graphene allotropes (GAs) for H-coverage spanning the entire range (0-100%). Four allotropes (graphyne, cyclic graphene, octagonal graphene, and biphenylene) with larger unit lattice size than graphene are considered. The effect of the degree of functionalization and molecular structure on the Young's modulus and strength are investigated, and the failure processes of some new GAs are reported for the first time. We show that the mechanical properties of the hydrogenated GAs deteriorate drastically with increasing H-coverage within the sensitive threshold, beyond which the mechanical properties remain insensitive to the increase in H-coverage. This drastic deterioration arises both from the conversion of sp2 to sp3 bonding and easy rotation of unsupported sp3 bonds. Allotropes with different lattice structures correspond to different sensitive thresholds. The Young's moduli deterioration of fully hydrogenated allotropes can be up to 70% smaller than that of the corresponding pristine structure. Moreover the tensile strength shows an even larger drop of about 90% and higher sensitivity to H-coverage even if it is small. Our results suggest that the unique coverage-dependent deterioration of the mechanical properties must be taken into account when analyzing the performance characteristics of nanodevices fabricated from functionalized GAs.

cond-mat.mtrl-sci↗