O gęstościowej hipotezie Sarnaka

• Autorzy: Lemańczyk Mariusz

Warianty tytułu

EN

On Sarnak’s conjecture

• Języki publikacji: PL
• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Wiadomości Matematyczne
• Rocznik: 2020
• Tom: T. 56, Nr 2
• Strony: 179--196
• Opis fizyczny: Bibliogr. 38 poz.

Twórcy

autor

Lemańczyk Mariusz

• Wydział Matematyki i Informatyki Uniwersytet Mikołaja Kopernika

• https://orcid.org/0000-0002-1502-5978

Bibliografia

• [1] E. H. El Abdalaoui, J. Kułaga-Przymus, M. Lemańczyk, T. de la Rue, The Chowla and the Sarnak conjectures from ergodic theory point of view, Discrete Contin. Dyn. Syst. 37 (2017), 2899–2944.
• [2] E. H. El Abdalaoui, J. Kułaga-Przymus, M. Lemańczyk, T. de la Rue, Möbius disjointness for models of an ergodic system and beyond, Israel J. Math. 228 (2018), 707–751.
• [3] A. S. Besicovitch, On the density of certain sequences of integers, Math. Ann. 110 (1935), 336–341.
• [4] E. Bessel-Hagen, Zahlentheorie, Teubner, Leipzig 1929.
• [5] J. Bourgain, P. Sarnak, T. Ziegler, Disjointness of Möbius from horocycle flows, t. 28, Springer, New York 2013.
• [6] S. Chowla, On abundant numbers, J. Indian Math. Soc., New Ser. 1 (1934), 41–44.
• [7] S. Chowla, The Riemann hypothesis and Hilbert’s tenth problem, Mathematics and Its Applications, t. 4, Gordon and Breach Science Publishers, New York 1965.
• [8] A. Cobham, Uniform tag sequences, Math. Systems Feory 6 (1972), 164–192.
• [9] H. Davenport, Über numeri abundantes, Sitzungsber. Preuss. Akad. Wiss. (1933), 830–837.
• [10] H. Davenport, P. Erdős, On sequences of positive integers, Acta Arith. 2 (1936), 147–151.
• [11] M. Denker, C. Grillenberger, K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Math., t. 527, Springer, New York 1976.
• [12] T. Downarowicz, Entropy in Dynamical Systems, New Mathematical Monographs, t. 18, Cambridge University Press, Cambridge 2011.
• [13] P. Erdős, On the density of the abundant numbers, J. London Math. Soc. 9 (1934), 278–282.
• [14] S. Ferenczi, J. Kułaga-Przymus, M. Lemańczyk, Sarnak’s conjecture, what’s new, [w:] Ergodic theory and dynamical systems in their interactions with arithmetics and combinatorics (S. Ferenczi, J. Kułaga-Przymus, M. Lemańczyk, red.), Lecture Notes in Math., t. 2213, Springer, Cham, 163–235.
• [15] N. Frantzikinakis, The structure of strongly stationary systems, J. Anal. Math. 93 (2004), 359–388.
• [16] N. Frantzikinakis, B. Host, The logarithmic Sarnak conjecture for ergodic weights, Ann. of Math. 187 (2018), 869–931.
• [17] A. Gomilko, D. Kwietniak, M. Lemańczyk, Sarnak’s conjecture implies the Chowla conjecture along a subsequence, [w:] Ergodic theory and dynamical systems in their interactions with arithmetics and combinatorics (S. Ferenczi, J. Kułaga-Przymus, M. Lemańczyk, red.), Lecture Notes in Math., t. 2213, Springer, Cham, 237–247.
• [18] A. Gomilko, M. Lemańczyk, T. de la Rue, Möbius orthogonality in density for zero entropy dynamical systems, Pure and Applied Functional Analysis 5 (2020), 1357–1376.
• [19] B. Green, T. Tao, The Möbius function is strongly orthogonal to nilsequences, Ann. of Math. 175 (2012), nr 2, 541–566.
• [20] R. R. Hall, Sets of multiples, Cambridge Tracts in Math., t. 118, Cambridge University Press, Cambridge 1996.
• [21] W. Huang, Z. Wang, X. Ye, Measure complexity and Möbius disjointness, Adv. Math. 347 (2019), 827–858.
• [22] W. Huang, Z. Wang, G. Zhang, Möbius disjointness for topological models of ergodic systems with discrete spectrum, J. Modern Dynamics 14 (2019), 277–290.
• [23] A. Kanigowski, M. Lemańczyk, M. Radziwiłł, Rigidity in dynamics and Möbius disjointness, ukaże się w Fundamenta Mathematicae.
• [24] K. Matomäki, M. Radziwiłł, Multiplicative functions in short intervals, Ann. of Math. 183 (2016), nr 2, 1015–1056.
• [25] K. Matomäki, M. Radziwiłł, T. Tao, An averaged form of Chowla’s conjecture, Algebra Number Theory 9 (2015), 2167–2196.
• [26] K. Matomäki, M. Radziwiłł, T. Tao, J. Teräväinen, T. Ziegler, Higher uniformity of bounded multiplicative functions in short intervals on average, preprint.
• [27] C. Müllner, Automatic sequences fulfill the Sarnak conjecture, Duke Math. J. 166 (2017), 3219–3290.
• [28] M. Queffélec, Substitution dynamical systems. Spectral analysis, wyd. 2, Lecture Notes in Math., t. 1294, Springer, Dordrecht 2010.
• [29] O. Ramaré, Chowla’s conjecture: from the Liouville function to the Möbius function, [w:] Ergodic theory and dynamical systems in their interactions with arithmetics and combinatorics (S. Ferenczi, J. Kułaga-Przymus, M. Lemańczyk, red.), Lecture Notes in Math., t. 2213, Springer, Cham, 317–323.
• [30] W. Rudin, Functional analysis, wyd. 2, McGraw-Hill Inc., New York 1991.
• [31] P. Sarnak, Free lectures on the Möbius function, randomness and dynamics, dostępne pod adresem http://publications.ias.edu/sarnak/paper/512 (dostęp: 2020-10-22).
• [32] T. Tao, The Chowla conjecture and the Sarnak conjecture, dostępne pod adresem https://terrytao.wordpress.com/2012/10/14/the-chowla-conjecture-and-the-sarnak-conjecture (dostęp: 2020-10-22).
• [33] T. Tao, The logarithmically averaged Chowla and Elliot conjectures for two-point correlations, Forum Math. Pi 4 E8 (2016).
• [34] T. Tao, Equivalence of the logarithmically averaged Chowla and Sarnak conjectures, [w:] Number theory – diophantine problems, uniform distribution and applications (C. Elsholtz, P. Grabner, red.), Springer, Cham 2017, 391–421.
• [35] T. Tao, The logarithmically averaged and non-logarithmically averaged Chowla conjectures, dostępne pod adresem https://terrytao.wordpress.com/2017/10/20/the-logarithmically-averaged-and-non-logarithmically-averaged-chowla-conjectures/ (dostęp: 2020-10-22).
• [36] T. Tao, J. Teräväinen, Odd order cases of the logarithmically averaged Chowla conjecture, J. Féor. Nombres Bordeaux 30 (2018), 997–1015.
• [37] T. Tao, J. Teräväinen, Fe structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliot conjectures, Duke Math. J. 168 (2019), 1977–2027.
• [38] Z. Wang, Möbius disjointness for analytic skew products, Invent. Math. 209, 175–196.

Uwagi

PL

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