On multiple zeta values of level two
Web2. 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 ... Webinteresting part is about multiple zeta and alternating multiple zeta values, so I will establish notation for them rst. For positive integers i 1;:::; k with 1 >1, the corresponding multiple zeta value is the real number (i 1;i 2;:::;i k) = X n1>n2> >n k 1 1 ni1 1 n i2 2 n i k k: This can be generalized to alternating multiple zeta values with ...
On multiple zeta values of level two
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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 … 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 …
WebThe 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 … 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 …
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 … 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 ...
Webmultiple zeta values of maximal height. 2010 Mathematics subject classification: primary 11M32; secondary 11M41. Keywords and phrases: multiple zeta values, Arakawa–Kaneko zeta function. 1.Main results The multiple zeta value (MZV) is a real number given by the nested series (k 1;:::;k r) = X 0
Web31 de jan. de 2013 · For multiple zeta values, ζ (a, b) is expressible in terms of ordinary zeta values ζ (n) when a + b is odd. ... ... (unlike Eq. (10), this formula requires p to be odd). Eq. (11) was... thomas hannah bookWeb1 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. … ugg ascot bomber slippersWebEvery multiple zeta value (1:1) is a Q-linear combination of (1.2) f (n 1;:::;n r); where n 1;:::;n r2f2;3gg: In this paper we proveConjectures 1and 2using motivic multiple zeta values. These are elements in a certain graded comodule HMT+over the a ne ring of functions on the prounipotent part of G ugg arch supportWebWe 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 … thomas hannah massdepWeb10 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. … thomas hannah edinburghWebAbstract. 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 … ugg arch support slippers womensWeb1 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 … ugg ash fog