arXiv subjects
Publications and source records attributed to P. Akhilesh.
We study the distribution of square-full numbers under the assumptions of Riemann hypothesis and that the zeros of $\zeta(s)$ are simple. Thus the error term is improved to a considerable extent with an extra main term.
In this paper we introduce and study double tails of multiple zeta values. We show, in particular, that they satisfy certain recurrence relations and deduce from this a generalization of Euler's classical formula $ζ(2)=3\sum_{m=1}^\infty m^{-2}\left({2m\atop m}\right)^{-1}$ to all multiple zeta values, as well as a new and very efficient algorithm for computing these values.
In this paper, we formally introduce the notion of Ap{é}ry-like sums and we show that every multiple zeta values can be expressed as a $\bf Z$-linear combination of them. We even describe a canonical way to do so. This allows us to put in a new theoretical context several identities scattered in the literature, as well as to discover many new interesting ones. We give in this paper new integral formulas for multiple zeta values and Apéry-like sums. They enable us to give a short direct proof of Zagier's formulas for $ζ(2,\ldots,2,3,2,\ldots,2)$ as well as of similar ones in the context of Ap{é}ry-like sums. The relations between Apéry-like sums themselves still remain rather mysterious, but we get significant results and state some conjectures about their pattern.