Related papers: Log-sine evaluations of Mahler measures
We continue the analysis of higher and multiple Mahler measures using log-sine integrals as started in "Log-sine evaluations of Mahler measures" and "Special values of generalized log-sine integrals" by two of the authors. This motivates a…
It is known that multiple zeta values can be written in terms of certain iterated log-sine integrals. Conversely, we evaluate iterated log-sine integrals in terms of multiple polylogarithms and multiple zeta values in this paper. We also…
We introduce an iterated integral version of (generalized) log-sine integrals (iterated log-sine integrals) and prove a relation between a multiple polylogarithm and iterated log-sine integrals. We also give a new method for obtaining…
In this work we apply the techniques that were developed in [Lalin: An algebraic integration for Mahler measure] in order to study several examples of multivariable polynomials whose Mahler measure is expressed in terms of special values of…
We consider a generalization of the Mahler measure of a multivariable polynomial $P$ as the integral of $\log^k|P|$ in the unit torus, as opposed to the classical definition with the integral of $\log|P|$. A zeta Mahler measure, involving…
The Mahler measures of some n-variable polynomial families are given in terms of special values of the Riemann zeta function and a Dirichlet L-series, generalizing the results of \cite{L}. The technique introduced in this work also…
We present a new systematic method for evaluating generalized log-sine integrals in terms of polylogarithms. Our approach is based on an identity connecting ordinary generating functions of polylogarithms to integrals involving the sine…
By using the method of iterated integral representations of series, we establish some explicit relationships between multiple zeta values and Integrals of logarithmic functions. As applications of these relations, we show that multiple zeta…
We study generalized log-sine integrals at special values. At $\pi$ and multiples thereof explicit evaluations are obtained in terms of Nielsen polylogarithms at $\pm1$. For general arguments we present algorithmic evaluations involving…
The Mahler measures of certain polynomials of up to five variables are given in terms of multiple polylogarithms. Each formula is homogeneous and its weight coincides with the number of variables of the corresponding polynomial.
We present an exact formula for the Mahler measure of an infinite family of polynomials with arbitrarily many variables. The formula is obtained by manipulating the integral defining the Mahler measure using certain transformations,…
In this paper we prove some new identities for multiple zeta values and multiple zeta star values of arbitrary depth by using the methods of integral computations of logarithm function and iterated integral representations of series. By…
We study the Mahler measures of certain families of Laurent polynomials in two and three variables. Each of the known Mahler measure formulas for these families involves $L$-values of at most one newform and/or at most one quadratic…
In this paper we present a new family of identities for Euler sums and integrals of polylogarithms by using the methods of generating function and integral representations of series. Then we apply it to obtain the closed forms of all…
Five series are evaluated in terms of zeta values. Three of the series involve harmonic numbers and one involves Stirling numbers of the first kind. The evaluation of these series is reduced to the evaluation of certain integrals, including…
In this paper we consider iterated integrals of multiple polylogarithm functions and prove some explicit relations of multiple polylogarithm functions. Then we apply the relations obtained to find numerous formulas of alternating multiple…
We prove a kind of integral expressions for finite multiple harmonic sums and multiple zeta-star values. Moreover, we introduce a class of multiple integrals, associated with some combinatorial data (called 2-labeled posets). This class…
We prove several identities relating three-variable Mahler measures to integrals of inverse trigonometric functions. After deriving closed forms for most of these integrals, we obtain ten explicit formulas for three-variable Mahler…
Multiple $T$-values, a variant of multiple zeta values of level two, were introduced and studied by Kaneko and Tsumura. This paper will introduce iterated log-tangent integrals and discuss their relations with multiple $T$-values. We will…
There are many examples of several-variable polynomials whose Mahler measure is expressed in terms of special values of polylogarithms. These examples are expected to be related to computations of regulators, as observed by Deninger, and…