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. 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 …
Variants of multiple zeta values with even and odd summation
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 ... Web1 de ago. de 2024 · Finite colored multiple zeta values We recall that finite MZVs and finite Euler sums are elements of the Q -ring A: = ∏ p ∈ P F p / ⨁ p ∈ P F p. Note that for N = 1, 2, the set A can be identified with A ( N) since all primes greater than 2 are odd and we can safely disregard the prime p = 2. In the rest of this section, we assume N = 3, 4 or 6. slowest rap song
Zeta function regularization, the multiplicative anomaly and the ...
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. … Web7 de mai. de 2024 · The second author wishes to express his thanks to Herbert Gangl for drawing his attention to Yamamoto’s {1 \over 2} -interpolated multiple zeta values. The second author also thanks Max Planck Institute for Mathematics, where the paper was written, for the invitation and hospitality. 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 … slowest rate of diffusion