This is a sequel to [FJ]. It will give a more natural framework for constructing elements in the Hopf algebra χF of framed mixed Tate motives according to Bloch and Křiž [BK]. This framework allows us to extend the results of [FJ] to interpret all multiple zeta values (including the divergent ones) and the multiple polylogarithms in one variable as elements of χF . It implies that the pro-unipo...

We study point-sphere and point-plane incidences in three-dimensional space. In particular, for 1 < k < n, we say that a set of spheres (resp., planes) is k-non-degenerate if no circle is contained in k spheres of the set (resp., if no line is contained in k planes of the set). We prove that, for every ε > 0, the number of incidences between a set of m points and a k-non-degenerate set of n sph...

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We present a reformulation of the plane-wave pseudopotential method for insulators. This new approach allows us to perform density-functional calculations by solving directly for ‘‘nonorthogonal generalized Wannier functions’’ rather than extended Bloch states. We outline the theory on which our method is based and present test calculations on a variety of systems. Comparison of our results wit...

In this paper we will prove Goncharov’s 22-term relations (see [A.B. Goncharov, Geometry of configurations, polylogarithms and motivic cohomology, Adv. Math. 114 (1995) 179–319. [G1]]) in the linearized version of Bloch’s higher Chow group CH3(F,5) using linear fractional cycles of Bloch, Kriz and Totaro under the Beilinson–Soulé vanishing conjecture that CH2(F,n)= 0 for n 4. © 2006 Elsevier In...

Based on a novel application of an archimedean type pairing to the geometry and deformation theory of K3 surfaces, we construct a regulator indecomposable K1-class on a self-product of a K3 surface. In the Appendix, we explain how this pairing is a special instance of a general pairing on precycles in the equivalence relation defining Bloch’s higher Chow groups.

Patrik Wyss, Shaihan J Malik, Vincent O Boer, Johanna J Bluemink, Alexander Raaijmakers, Mustafa Cavusoglu, Peter Luijten, Johannes J Hoogduin, Giel Mens, and Anke Henning Institute for Biomedical Engineering, UZH and ETH Zurich, Zurich, Switzerland, Imaging Sciences and Biomedical Engineering, Kings College London, London, United Kingdom, University Medical Center Utrecht, Utrecht, Netherlands...

We give a characterization of lacunary series in the Bloch space of the unit ball in C in terms of Taylor coefficients. We also characterize Bloch functions whose Taylor coefficients are nonnegative. The corresponding problems for BMOA are discussed as well.

In this paper, we study algebraic and analytic properties of Fourier coefficients, expressed as q-series, of the so-called Bloch-Okounkov n-point function. We prove several results about these series and explain how they relate to Rogers’ false theta function. Then we obtain their full asymptotics, as τ → 0, and use this result to derive asymptotic properties of the coefficients in the q-expans...