Manuel Hauke
About
I am mainly working on (metric) Diophantine approximation and fine-scale statistics of sequences, with tools from analysis, number theory and probability theory, but I am always eager to explore new areas of mathematics that are related to number theory and uniform distribution.
I received my PhD degree under the supervision of Prof. Christoph Aistleitner at TU Graz. I was a Junior fellow for the program "Analytic number theory" at Institut Mittag-Leffler (Stockholm) and a Postdoctorate Research Associate at the University of York by Prof. Victor Beresnevich and Prof. Sanju Velani.
View my personal website here.
Publications
[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, 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. Henri Lebesgue, 7(2):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 arXiv version and the journal 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.)