On multiple zeta values of level two
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 … WebFor k ≤ n, let E ( 2 n, k) be the sum of all multiple zeta values with even arguments whose weight is 2 n and whose depth is k. Of course E ( 2 n, 1) is the value ζ ( 2 n) of the Riemann zeta function at 2 n, and it is well known that E ( 2 n, 2) = 3 4 ζ ( 2 n). Recently Shen and Cai gave formulas for E ( 2 n, 3) and E ( 2 n, 4) in terms of ...
On multiple zeta values of level two
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WebWe will mainly deal with three types of objects: Multiple zeta values (real numbers), modular forms (holomorphic func- tions in the complex upper half plane) and q-analogues of multiple zeta values (q-series with rational coe cients). http://www-personal.umich.edu/~francc/files/zeta_talk.pdf
WebAbstract. We introduce and study a \level two" analogue of nite multiple zeta values. We give conjectural bases of the space of nite Euler sums as well as that of usual nite … 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 …
Web1.2. Multiple zeta values. Now consider the product of two zeta values, (k) (l) = X m;n>0 1 mknl: Splitting the domain into three parts, Euler observed that (k) (l) = X m>n>0 + X n>m>0 + X m=n>0! 1 mknl: If one now takes products of zeta values with the above kind of double sums, one obtains triple sums of a similar shape. Iterating this ... Web1 de mar. de 2012 · A formula is given for the special multiple zeta values occurring in the title as rational linear combinations of products ζ ( m) π 2 n with m odd. The existence of …
Web1 de dez. de 2024 · On multiple zeta values of level two. We study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta …
WebThe 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. cineworld cineplexWeb1 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. … cineworld clerks 3WebWhen 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. cineworld cineplex dealWeb9 de mar. 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 … diagenetic rockshttp://javier.fresan.perso.math.cnrs.fr/mzv.pdf diagenesis of limestoneWebON MULTIPLE ZETA VALUES OF LEVEL TWO MASANOBU KANEKO AND HIROFUMI TSUMURA Abstract. We study a variant of multiple zeta values of level 2, which forms … cineworld closedWebThe multiplicative anomaly associated with the zeta-function regularized determinant is computed for the Laplace-type operators V1=−Δ+V1 and V2=−Δ+V2, with V1, V2 constant, in a D-dimensional compact smooth manifold MD, making use of several results due to Wodzicki and by direct calculations in some explicit examples. It is found that the … cineworld cinema weston super mare