اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدExplicit Relations between Multiple Zeta Values and Related Variants
72
0
0.0
(
0
)
تأليف
Ce Xu
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper we present some new identities for multiple polylogarithms (abbr. MPLs) and multiple harmonic star sums (abbr. MHSSs) by using the methods of iterated integral computations of logarithm functions. Then, by applying these formulas obtained, we establish some explicit relations between Kaneko-Yamamoto type multiple zeta values (abbr. K-Y MZVs), multiple zeta values (abbr. MZVs) and MPLs. Further, we find some explicit relations between MZVs and multiple zeta star values (abbr. MZSVs). Furthermore, we define an Ap{e}ry-type variant of MZSVs $zeta^star_B({bf k})$ (called multiple zeta $B$-star values, abbr. MZBSVs) which involve MHSSs and central binomial coefficients, and establish some explicit connections among MZVs, alternating MZVs and MZBSVs by using the method of iterated integrals. Finally, some interesting consequences and illustrative examples are presented.
قيم البحث
اقرأ أيضاً
In this paper, we study some Euler-Apery-type series which involve central binomial coefficients and (generalized) harmonic numbers. In particular, we establish elegant explicit formulas of some series by iterated integrals and alternating multiple z
eta values. Based on these formulas, we further show that some other series are reducible to ln(2), zeta values, and alternating multiple zeta values by considering the contour integrals related to gamma functions, polygamma functions and trigonometric functions. The evaluations of a large number of special Euler-Apery-type series are presented as examples.
In this paper we show that in perturbative string theory the genus-one contribution to formal 2-point amplitudes can be related to the genus-zero contribution to 4-point amplitudes. This is achieved by studying special linear combinations of multiple
zeta values that appear as coefficients of the amplitudes. We also exploit our results to relate closed strings to open strings at genus one using Browns single-valued projection, proving a conjecture of Broedel, Schlotterer and the second author.
We use the Arakawa-Berndt theory of generalized eta-functions to prove a conjecture of Lal`in, Rodrigue and Rogers concerning the algebraic nature of special values of the secant zeta functions.
We make explicit an argument of Heath-Brown concerning large and small gaps between nontrivial zeroes of the Riemann zeta-function, $zeta(s)$. In particular, we provide the first unconditional results on gaps (large and small) which hold for a positi
ve proportion of zeroes. To do this we prove explicit bounds on the second and fourth power moments of $S(t+h)-S(t)$, where $S(t)$ denotes the argument of $zeta(s)$ on the critical line and $h ll 1 / log T$. We also use these moments to prove explicit results on the density of the nontrivial zeroes of $zeta(s)$ of a given multiplicity.
In a recent paper, A. Libgober showed that the multiplicative sequence {Q_i(c_1,...,c_i)} of Chern classes corresponding to the power series Q(z)=1/Gamma(1+z) appears in a relation between the Chern classes of certain Calabi-Yau manifolds and the per
iods of their mirrors. We show that the polynomials Q_i can be expressed in terms of multiple zeta values.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
