Research

Research Articles:

[25] M. Hauke and F. A. Ramírez: Twisted approximation with restricted denominators, submitted.
(Here is the arXiv version.)

[24] M. Hauke: The bad and rough rotation is Poissonian.
(Here is the arXiv version.)

[23] S. Chow, M. Hauke, A. Pollington and F. A. Ramírez: General Duffin-Schaeffer-type counterexamples in diophantine approximation, submitted.
(Here is the arXiv version.)

[22] C. Aistleitner, L. Frühwirth, M. Hauke and M. Manskova: Moment generating functions and moderate deviation principles for lacunary trigonometric sums,  Probab. Theory Relat. Fields, to appear.
(Here is the arXiv version.)

[21] M. Hauke and E. Kowalski: Rational approximation with chosen numerators, submitted.
(Here is the arXiv version.)

[20] L. Frühwirth and M. Hauke: On a Problem of Kac concerning Anisotropic Lacunary Sums, submitted.
(Here is the arXiv version.)

[19] M. Hauke and F. A. Ramírez: The Duffin-Schaeffer conjecture with a moving target, submitted.
(Here is the arXiv version.)

[18] V. Beresnevich, M. Hauke, and S. Velani: Borel-Cantelli, zero-one laws and inhomogeneous Duffin-Schaeffer, submitted.
(Here is the arXiv version.)

[17] M. Hauke and A. Zafeiropoulos: On inhomogeneous Poissonian Pair Correlations, Math. Proc. Camb. Philos. Soc. 2015,179(1):17-27.
(Here are the journal version and the arXiv version.)

[16] M. Hauke, S. Vazquez, and 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, Random Struct. Algorithms 66(1) (2025), e21265.
(Here are the journal version and the arXiv version.)

[13] D. Gayfulin and M. Hauke: Hausdorff dimension estimates for Sudler products with positive lower bound, Nonlinearity 38 (2025), 065008.
(Here are the journal version and the arXiv version.)

[12]  M. Hauke: Quantitative inhomogeneous Diophantine approximation for systems of linear forms, Proc. Am. Math. Soc. 153 (2025), 1867-1880.
(Here are the journal version and the arXiv version.)

[11]  B. Borda, L. Frühwirth and M. Hauke: Limit laws for cotangent and Diophantine sums, Selecta Math. 31:53 (2025).
(Here are the journal version and the arXiv version.)

[10] L. Frühwirth and M. Hauke: On Birkhoff sums that satisfy no temporal distributional limit theorem for almost every irrational, Ann. Henri Lebesgue 7(2) (2024), 251-265.
(Here are the journal version and 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. (2024).
(Here are the journal version and 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.)

Other publications:

M. Hauke: A century of metric Diophantine approximation and half a decade since Koukoulopoulos-Maynard (survey article for Internationale Mathematische Nachrichten, 257:1-29).
(Here are the journal version and the arXiv version).

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

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

Scientific Talks:

1.7.2025: Speaker at Journée d’Arithmétique 2025, University of Luxembourg on "The bad and rough rotation is Poissonian" (paper [24])

11.6.2025: Invited speaker at “York25 - Diophantine approximation and related fields” on "Diophantine approximation with prime denominator" (papers [21,24])

27.3.2025: Invited speaker at the Number Theory seminar at TU Graz on "Diophantine approximation with prime denominator" (paper [21]).

13.3.2025: Online Seminar talk in Diophantine Approximation and Related Topics on "Approximation by prime denominators: Twisted Diophantine approximation and approximation with chosen numerators" (paper [21]).
Find a video recording here.

10.12.2024: Invited speaker at the Analysis seminar of the University of Passau on "An introduction to metric Diophantine approximation".

6.12.2024: Invited speaker at the Workshop on Diophantine Approximation at TU Graz on "Littlewood meets Duffin and Schaeffer".

29.11.2024: Invited speaker in the Number theory seminar at ETH Zürich on "Metric Diophantine approximation: What comes after Duffin-Schaeffer?"

8.10.2024: Talk in the New England Dynamics and Number Theory seminar (NEDNT) on "Metric Diophantine approximation: Moving targets and inhomogeneous variants".

11.9.2024 + 25.9.2024: Talk in the Analysis seminar at NTNU Trondheim on "Metric number theory and Diophantine approximation - the past, the present, and the future".

19.6.2024: Talk in the Number Theory seminar at the University of York on "Proving Duffin-Schaeffer in an hour - an argument without quality" (paper [16]).

10.6.2024: Invited speaker for the Oxford Junior Number Theory Seminar on "Duffin-Schaeffer meets Littlewood and related topics" (paper [15]).

1.5.2024: Invited speaker for the London Number Theory Seminar at King's College London on "Duffin-Schaeffer meets Littlewood and related topics" (paper [15]).

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).

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 ).

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).

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).

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).

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

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).