picture Frederik Broucke

Frederik Broucke

Researcher in mathematics

Publications

Preprints

Published articles

  1. F. Broucke, T. Hilberdink, A mean value theorem for general Dirichlet series, Quart. J. Math. article haae051 (2024). [Article | Preprint]
  2. F. Broucke, G. Debruyne, Sz. Révész, Some examples of well-behaved Beurling number systems, to appear in Trans. Amer. Math. Soc. [Article | Preprint]
  3. F. Broucke, J. Vindas, A new generalized prime random approximation procedure and some of its applications, Math. Z. 307, 62 (2024). [Article | Preprint]
  4. F. Broucke, S. Weishäupl, On the Lindelöf hypothesis for general sequences, Mathematika 70 (2024), no. 2, e12240. [Article | Preprint]
  5. F. Broucke, T. Hilberdink, An omega-result for Beurling generalized integers, Acta Arith. 212 (2024), 359-371. [Article | Preprint]
  6. F. Broucke, A. Kouroupis, K.-M. Perfekt, A note on Bohr's theorem for Beurling integer systems, Math. Ann. 389 (2024), 4319–4333. [Article | Preprint]
  7. F. Broucke, J. Vindas, The pointwise behavior of Riemann's function, J. Fractal Geom. 10 (2023), no. 3/4, 333-349. [Article | Preprint]
  8. F. Broucke, G. Debruyne, On zero-density estimates and the PNT in short intervals for Beurling generalized numbers, Acta Arith. 207 (2023), 365-391. [Article | Preprint]
  9. F. Broucke, Lj. Oparnica, Distributed-order time-fractional wave equations, Z. Angew. Math. Phys. 74:1 article 19 (2023). [Article | Preprint]
  10. F. Broucke, G. Debruyne, J. Vindas, The optimal Malliavin-type remainder for Beurling generalized integers, J. Inst. Math. Jussieu. 23(1) (2024), 249-278 [Article | Preprint]
  11. F. Broucke, Lj. Oparnica, Micro-local and qualitative analysis of the fractional Zener wave equation, J. Differ. Equ. 321 (2022), 217-257. [Article | Preprint]
  12. F. Broucke, Note on a conjecture of Bateman and Diamond concerning the abstract PNT with Malliavin-type remainder, Monatsh. Math. 196 (2021), no. 3, 457-470. [Article | Preprint]
  13. F. Broucke, G. Debruyne, J. Vindas, On the absence of remainders in the Wiener-Ikehara and Ingham-Karamata theorems: a constructive approach, Proc. Amer. Math. Soc. 149 (2021), 1053-1060. [Article | Preprint]
  14. F. Broucke, G. Debruyne, J. Vindas, An asymptotic analysis of the Fourier-Laplace transforms of certain oscillatory functions, J. Math. Anal. Appl. 494 (2021), article number 124450. [Article | Preprint]
  15. F. Broucke, G. Debruyne, J. Vindas, Beurling integers with RH and large oscillation, Adv. Math. 370 (2020), article number 107240. [Article | Preprint]

Ph.D thesis

F. Broucke, Asymptotic methods in number theory and analysis, Dissertation, Ghent University, 2022. [pdf]