@article{12210,
  abstract     = {The aim of this paper is to find new estimates for the norms of functions of a (minus) distinguished Laplace operator L on the ‘ax+b’ groups. The central part is devoted to spectrally localized wave propagators, that is, functions of the type ψ(L−−√)exp(itL−−√), with ψ∈C0(R). We show that for t→+∞, the convolution kernel kt of this operator satisfies
∥kt∥1≍t,∥kt∥∞≍1,
so that the upper estimates of D. Müller and C. Thiele (Studia Math., 2007) are sharp. As a necessary component, we recall the Plancherel density of L and spend certain time presenting and comparing different approaches to its calculation. Using its explicit form, we estimate uniform norms of several functions of the shifted Laplace-Beltrami operator Δ~, closely related to L. The functions include in particular exp(−tΔ~γ), t>0,γ>0, and (Δ~−z)s, with complex z, s.},
  author       = {Akylzhanov, Rauan and Kuznetsova, Yulia and Ruzhansky, Michael and Zhang, Haonan},
  issn         = {1432-1823},
  journal      = {Mathematische Zeitschrift},
  keywords     = {General Mathematics},
  number       = {4},
  pages        = {2327--2352},
  publisher    = {Springer Nature},
  title        = {{Norms of certain functions of a distinguished Laplacian on the ax + b groups}},
  doi          = {10.1007/s00209-022-03143-z},
  volume       = {302},
  year         = {2022},
}

@article{9260,
  abstract     = {We study the density of rational points on a higher-dimensional orbifold (Pn−1,Δ) when Δ is a Q-divisor involving hyperplanes. This allows us to address a question of Tanimoto about whether the set of rational points on such an orbifold constitutes a thin set. Our approach relies on the Hardy–Littlewood circle method to first study an asymptotic version of Waring’s problem for mixed powers. In doing so we make crucial use of the recent resolution of the main conjecture in Vinogradov’s mean value theorem, due to Bourgain–Demeter–Guth and Wooley.},
  author       = {Browning, Timothy D and Yamagishi, Shuntaro},
  issn         = {1432-1823},
  journal      = {Mathematische Zeitschrift},
  pages        = {1071–1101},
  publisher    = {Springer Nature},
  title        = {{Arithmetic of higher-dimensional orbifolds and a mixed Waring problem}},
  doi          = {10.1007/s00209-021-02695-w},
  volume       = {299},
  year         = {2021},
}