On multiple zeta values of level two
WebWhen all of the are n th roots of unity and the are all nonnegative integers, the values of the multiple polylogarithm are called colored multiple zeta values of level. In particular, when n = 2 {\displaystyle n=2} , they are called Euler sums or alternating multiple zeta values , and when n = 1 {\displaystyle n=1} they are simply called multiple zeta values. Web1 de jan. de 2013 · Introduction and main results Double zeta values of level 2 are deï¬ ned by ζ o(r, s)= ∑ m>n>0 m,n:odd 1 mrns , (1) here r, s are positive integers with r 2. …
On multiple zeta values of level two
Did you know?
Web17 de abr. de 2024 · We study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is regarded as the `shuffle counterpart' of Hoffman's `odd variant', exhibits nice properties such as duality, shuffle product, parity results, etc., like WebWe study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is regarded as the ‘shuffle …
Web10 de ago. de 2024 · M. Kaneko and H. Tsumura, Zeta functions connecting multiple zeta values and poly-Bernoulli numbers, Adv. Stud. Pure Math. 84, 2024, pp. 181-204. … WebWe study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is regarded as the `shuffle …
WebThus, each value (2k) is a rational multiple of ˇ2k. If that isn’t surprising to you, be aware of the following: the odd values (2k + 1) are not expected to be related to ˇin any signi cant algebraic way. Why the even zeta values (2k) are algebraically related to ˇand the odd values (2k + 1) are (probably) not is one unsolved Web19 de nov. de 2024 · We first review our previous works of Arakawa and the authors on two, closely related single-variable zeta functions. Their special values at positive and …
WebWe study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is regarded as the `shuffle counterpart' of Hoffman's `odd variant', exhibits nice properties such as duality, shuffle product, parity results, etc., like ordinary multiple zeta values. We also give some …
Weba level 2 multiple zeta value because of the congruence condition in the summation and of the (easily proved) fact that this value can be written as a linear combination of … small saws for cutting woodWeb2. Open-string tree-level amplitudes Open-string amplitudes at tree-level are obtained from correlators on a genus-zero Riemann ... 1gexclusively, which in turn can be cast into multiple zeta values using eq. (2.5). As an example, the string correction to the five-point amplitude2 for the trivial permutation reads F23 =1 z(2)(s 12s 23 +s 12s ... highpeak energy incWebUpdated Mars 2, 2024 MZV IMSc 2011 1.2 Multizeta values: Zagier’s conjecture The situation changes drastically if we enlarge our set so as to include the so-called Multiple Zeta Values (MZV, also called Polyzeta values, Euler-Zagier numbers or multiple harmonic series): (s 1;:::;s k) = X n 1>n 2> >n k 1 1 n s 1 1 nk k which are de ned for k ... small saw horseWeb2 M. RAM MURTY AND KANEENIKA SINHA This Hurwitz zeta function, originally defined for Re(s) > 1, can also be ex-tended analytically for all s ∈ C, apart from s =1, where it has a simple pole with residue 1. In his study of ζ(s;x), Hurwitz was motivated by the problem of analytic continution of Dirichlet L-functions.For any Dirichlet character χ (mod q), we may … highpeakcoWeb26 de set. de 2024 · In this paper we present some new identities of hypergeometric type for multiple harmonic sums whose indices are the sequences $(\{1\}^a,c,\{1\}^b),$ … small saw to cut trimhttp://javier.fresan.perso.math.cnrs.fr/mzv.pdf small saws handheld cordlessWebThe zeta function values listed below include function values at the negative even numbers (s= −2, −4, etc.), for which ζ(s) = 0and which make up the so-called trivial zeros. The Riemann zeta functionarticle includes a colour plot illustrating how the function varies over a continuous rectangular region of the complex plane. small sawtimber