Research

Articles:

[17) M. Hauke, and A. Zafeiropoulos: On inhomogeneous Poissonian Pair Correlations, submitted.
(Here is the arXiv version.)

[16] M. Hauke, S.V. Saez, A. Walker: Proving the Duffin-Schaeffer conjecture without GCD graphs, submitted.
(Here is the arXiv version.)

[15] L. Frühwirth and M. Hauke: The Duffin-Schaeffer conjecture for multiplicative Diophantine approximation, submitted.
(Here is the arXiv version.)

[14] C. Aistleitner, M. Hauke, and A. Zafeiropoulos: On sequences with exponentially distributed gaps, submitted.
(Here is the arXiv version.)

[13] D. Gayfulin and M. Hauke: Hausdorff dimension estimates for Sudler products with positive lower bound, submitted.
(Here is the arXiv version.)

[12]  M. Hauke: Quantitative inhomogeneous Diophantine approximation for systems of linear forms, submitted.
(Here is the arXiv version.)

[11]  B. Borda, L. Frühwirth and M. Hauke: Limit laws for cotangent and Diophantine sums, submitted.
(Here is the arXiv version.)

[10] L. Frühwirth and M. Hauke: On Birkhoff sums that satisfy no temporal distributional limit theorem for almost every irrational, Ann. H. Lebesgue, to appear. (Here is the arXiv version.)

[9] L. Frühwirth and M. Hauke: On the metric upper density of Birkhoff sums for irrational rotations, Nonlinearity 36 (2023), 7065.
(Here are the journal version and the arXiv version.)

[8] C. Aistleitner, B. Borda, and M. Hauke: On the distribution of partial quotients of reduced fractions with fixed denominator, Trans. Am. Math. Soc. 377(2) (2024), 1371–1408.
(Here are the journal version and the arXiv version.)

[7] M. Hauke: On the asymptotic behaviour of Sudler products for badly approximable numbers, J. Math. Anal. Appl. 531(1) (2024), 127737.
(Here are the journal version and the arXiv version.)

[6] M. Hauke, L. Lamster, R. Lüftenegger, and C. Rechberger: A Signature-Based Gröbner Basis Algorithm with Tail-Reduced Reductors (M5GB), submitted.
(Here is the arXiv version.)

[5] M. Hauke: Metric density results for the value distribution of Sudler products, Proc. Am. Math. Soc. 151 (2023), 2339-2351.
(Here are the journal version and the arXiv version.)

[4] C. Aistleitner, B. Borda, and M. Hauke: On the metric theory of approximations by reduced fractions: a quantitative Koukoulopoulos-Maynard theorem, Compos. Math. 159(2) (2023), 207-231.
(Here are the journal version  and the arXiv version.)

[3] M. Hauke, and A. Zafeiropoulos: Weak Poissonian Correlations, Ann. Mat. Pura Appl., to appear.
(Here is the arXiv version.)

[2] M. Hauke: On extreme values for the Sudler product of quadratic irrationals, Acta. Arith. 204 (2022), 41-82.
(Here are the journal version and the arXiv version.)

[1] M. Hauke, and A. Zafeiropoulos: Poissonian correlations of higher orders, J. Number Theory 243 (2023), 202-240.
(Here are the journal version and the arXiv version.)

Theses:

M. Hauke: Signature Gröbner bases A comprehensive survey and a new algorithmic approach (MSc thesis).

M. Hauke: Analytic methods in Diophantine approximation and Poissonian correlations (PhD thesis).

Scientific Talks: 

20.07.2022: Talk in a Special Session at the MCQMC 2022 in Linz on "The metric theory of approximations by reduced fractions: Quantifying the Duffin-Schaeffer conjecture" (paper [4], download slides here).

29.11.2022: Online Talk at the One World Numeration seminar (OWNS) on Sudler products (papers [2],[5],[7]), for a video recording
and presentation slides see here.

12.2.2023: Workshop Talk at Diophantine Analysis, Dynamics and Related Topics at Technion, Haifa, Israel on "The metric theory of approximations by reduced fractions: Quantifying the Duffin-Schaeffer conjecture" (paper [4], download slides here).

4.7.2023: Talk in a Special Session at the Journee d'Arithmetique 2023 on "The distribution of partial quotients of reduced fractions with fixed denominator" (paper [8], download slides here).

6.11.2023: Talk in the Number Theory seminar at the University of York on "Birkhoff sums and metric Diophantine Approximation" (papers [9] and [10], download slides here).

13.11.2023: Invited speaker in the Number Theory seminar at the University of Warwick on "Birkhoff sums and metric Diophantine Approximation" (papers [9] and [10], download slides here ).

9.2.2024: Talk at Institute Mittag-Leffler on "The Duffin-Schaeffer conjecture and beyond" (papers [4] and [12], download slides here, video recording here).

1.5.2024 (scheduled): Invited speaker in the London Number Theory Seminar at King's College London on "Duffin-Schaeffer meets Littlewood and related topics".