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Let $X_0^{star}(k,n,s)$ denote the sum of all multiple zeta-star values of weight $k$, depth $n$ and height $s$. Kaneko and Ohno conjecture that for any positive integers $m,n,s$ with $m,ngeqslant s$, the difference $(-1)^mX_0^{star}(m+n+1,n+1,s)-(-1)^nX_0^{star}(m+n+1,m+1,s)$ can be expressed as a polynomial of zeta values with rational coefficients. We give a proof of this conjecture in this paper.
By using various expansions of the parametric digamma function and the method of residue computations, we study three variants of the linear Euler sums, related Hoffmans double $t$-values and Kaneko-Tsumuras double $T$-values, and establish several s
It is well known that for any prime $pequiv 3$ (mod $4$), the class numbers of the quadratic fields $mathbb{Q}(sqrt{p})$ and $mathbb{Q}(sqrt{-p})$, $h(p)$ and $h(-p)$ respectively, are odd. It is natural to ask whether there is a formula for $h(p)/h(
In this short note we confirm the relation between the generalized $abc$-conjecture and the $p$-rationality of number fields. Namely, we prove that given K$/mathbb{Q}$ a real quadratic extension or an imaginary $S_3$-extension, if the generalized $ab
We show that for a monic polynomial $f(x)$ over a number field $K$ containing a global permutation polynomial of degree $>1$ as its composition factor, the Newton Polygon of $fmodmathfrak p$ does not converge for $mathfrak p$ passing through all fini
We use logarithmic {ell}-class groups to take a new view on Greenbergs conjecture about Iwasawa {ell}-invariants of a totally real number field K. By the way we recall and complete some classical results. Under Leopoldts conjecture, we prove that Gre