@article{19496,
  abstract     = {We introduce the notions of scale for sets and measures on metric space by generalizing the usual notions of dimension. Several versions of scales are introduced such as Hausdorff, packing, box, local and quantization. They are defined for different growth, allowing a refined study of infinite dimensional spaces. We prove general theorems comparing the different versions of scales. They are applied to describe geometries of ergodic decompositions, of the Wiener measure and from functional spaces. The first application solves a problem of Berger on the notions of emergence (2020); the second lies in the geometry of the Wiener measure and extends the work of Dereich–Lifshits (2005); the last refines Kolmogorov–Tikhomirov (1958) study on finitely differentiable functions.},
  author       = {Helfter, Mathieu},
  issn         = {1432-1823},
  journal      = {Mathematische Zeitschrift},
  publisher    = {Springer Nature},
  title        = {{Scales}},
  doi          = {10.1007/s00209-025-03719-5},
  volume       = {310},
  year         = {2025},
}

@article{19776,
  abstract     = {We use the circle method to prove that a density 1 of elements in Fq[t] are representable as a sum of three cubes of essentially minimal degree from Fq[t], assuming the Ratios Conjecture and that char(Fq)>3. Roughly speaking, to do so, we upgrade an order of magnitude result to a full asymptotic formula that was conjectured by Hooley in the number field setting.},
  author       = {Browning, Timothy D and Glas, Jakob and Wang, Victor},
  issn         = {1432-1823},
  journal      = {Mathematische Zeitschrift},
  number       = {4},
  publisher    = {Springer Nature},
  title        = {{Optimal sums of three cubes in Fq[t]}},
  doi          = {10.1007/s00209-025-03765-z},
  volume       = {310},
  year         = {2025},
}

@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{19492,
  abstract     = {Kuroda’s formula relates the class number of a multiquadratic number field K to the class numbers of its quadratic subfields ki. A key component in this formula is the unit group index (math formular). We study how Q(K) behaves on average in certain natural families of totally real biquadratic fields K parametrized by prime numbers.},
  author       = {Chan, Yik Tung and Milovic, Djordjo},
  issn         = {1432-1823},
  journal      = {Mathematische Zeitschrift},
  number       = {2},
  pages        = {1509--1527},
  publisher    = {Springer Nature},
  title        = {{Kuroda’s formula and arithmetic statistics}},
  doi          = {10.1007/s00209-021-02823-6},
  volume       = {300},
  year         = {2021},
}

@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},
}