Zhao, Xuan; Shen, Luming Localized growth speed of the digits in Engel expansions. (English) Zbl 07762425 J. Math. Anal. Appl. 530, No. 2, Article ID 127657, 9 p. (2024). Reviewer: Takao Komatsu (Hangzhou) MSC: 11K55 28A80 PDFBibTeX XMLCite \textit{X. Zhao} and \textit{L. Shen}, J. Math. Anal. Appl. 530, No. 2, Article ID 127657, 9 p. (2024; Zbl 07762425) Full Text: DOI
Szewczak, Zbigniew; Weber, Michel Classical and almost sure local limit theorems. (English) Zbl 07800604 Diss. Math. 589, 1-97 (2023). MSC: 60-02 60F05 11K50 60F15 60G50 60J05 PDFBibTeX XMLCite \textit{Z. Szewczak} and \textit{M. Weber}, Diss. Math. 589, 1--97 (2023; Zbl 07800604) Full Text: DOI arXiv
Berkes, István; Borda, Bence Random walks on the circle and Diophantine approximation. (English) Zbl 07731126 J. Lond. Math. Soc., II. Ser. 108, No. 2, 409-440 (2023). Reviewer: Christoph Aistleitner (Graz) MSC: 11K38 11K60 60J05 60G50 PDFBibTeX XMLCite \textit{I. Berkes} and \textit{B. Borda}, J. Lond. Math. Soc., II. Ser. 108, No. 2, 409--440 (2023; Zbl 07731126) Full Text: DOI arXiv
Bettin, Sandro; Drappeau, Sary Limit laws for rational continued fractions and value distribution of quantum modular forms. (English) Zbl 07740421 Proc. Lond. Math. Soc. (3) 125, No. 6, 1377-1425 (2022). MSC: 11A55 37C30 11F03 11F67 60F05 PDFBibTeX XMLCite \textit{S. Bettin} and \textit{S. Drappeau}, Proc. Lond. Math. Soc. (3) 125, No. 6, 1377--1425 (2022; Zbl 07740421) Full Text: DOI arXiv OA License
Moroz, M. P. Gauss-Kuzmin problem for the difference Engel-series representation of real numbers. (English. Ukrainian original) Zbl 1509.11073 Ukr. Math. J. 74, No. 7, 1149-1154 (2022); translation from Ukr. Mat. Zh. 74, No. 7, 1004-1008 (2022). Reviewer: Manuel Hauke (Graz) MSC: 11K55 11J70 11K50 PDFBibTeX XMLCite \textit{M. P. Moroz}, Ukr. Math. J. 74, No. 7, 1149--1154 (2022; Zbl 1509.11073); translation from Ukr. Mat. Zh. 74, No. 7, 1004--1008 (2022) Full Text: DOI
Berend, Daniel; Kumar, Rishi Consecutive ratios in second-order linear recurrence sequences. (English) Zbl 1517.11007 Unif. Distrib. Theory 17, No. 2, 51-76 (2022). Reviewer: Raghib Abu-Saris (Edmonton) MSC: 11B37 39A06 PDFBibTeX XMLCite \textit{D. Berend} and \textit{R. Kumar}, Unif. Distrib. Theory 17, No. 2, 51--76 (2022; Zbl 1517.11007) Full Text: DOI
Chevallier, Nicolas The natural extension of the Gauss map and the Hermite best approximations. (English. French summary) Zbl 1508.11073 J. Théor. Nombres Bordx. 34, No. 2, 619-636 (2022). Reviewer: Oleg Karpenkov (Liverpool) MSC: 11J70 37A44 PDFBibTeX XMLCite \textit{N. Chevallier}, J. Théor. Nombres Bordx. 34, No. 2, 619--636 (2022; Zbl 1508.11073) Full Text: DOI arXiv
Chow, Sam; Zafeiropoulos, Agamemnon Fully inhomogeneous multiplicative Diophantine approximation of badly approximable numbers. (English) Zbl 07738335 Mathematika 67, No. 3, 639-646 (2021). Reviewer: Simon Kristensen (Aarhus) MSC: 11J83 11J70 28A78 PDFBibTeX XMLCite \textit{S. Chow} and \textit{A. Zafeiropoulos}, Mathematika 67, No. 3, 639--646 (2021; Zbl 07738335) Full Text: DOI arXiv
Zhang, Zhenliang; Tan, Xiaoyan The relative convergence speed for Engel expansions and Hausdorff dimension. (English) Zbl 1483.11164 Fractals 29, No. 4, Article ID 2150106, 7 p. (2021). MSC: 11K55 28A80 PDFBibTeX XMLCite \textit{Z. Zhang} and \textit{X. Tan}, Fractals 29, No. 4, Article ID 2150106, 7 p. (2021; Zbl 1483.11164) Full Text: DOI
Bugeaud, Yann; Kim, Dong Han; Lee, Seul Bee On the Lévy constants of Sturmian continued fractions. (English) Zbl 1491.11009 Pac. J. Math. 315, No. 1, 1-25 (2021). Reviewer: Jean-Marc Deshouillers (Bordeaux) MSC: 11A55 68R15 PDFBibTeX XMLCite \textit{Y. Bugeaud} et al., Pac. J. Math. 315, No. 1, 1--25 (2021; Zbl 1491.11009) Full Text: DOI arXiv
Lutz, Jack H.; Mayordomo, Elvira Computing absolutely normal numbers in nearly linear time. (English) Zbl 1521.11085 Inf. Comput. 281, Article ID 104746, 12 p. (2021). MSC: 11Y16 11K16 68Q17 68W32 PDFBibTeX XMLCite \textit{J. H. Lutz} and \textit{E. Mayordomo}, Inf. Comput. 281, Article ID 104746, 12 p. (2021; Zbl 1521.11085) Full Text: DOI arXiv
Sun, Peng A generalization of the Gauss-Kuzmin-Wirsing constant. (English) Zbl 1483.11142 Monatsh. Math. 196, No. 4, 911-925 (2021). Reviewer: Symon Serbenyuk (Kyïv) MSC: 11J70 11K50 37C30 PDFBibTeX XMLCite \textit{P. Sun}, Monatsh. Math. 196, No. 4, 911--925 (2021; Zbl 1483.11142) Full Text: DOI arXiv
Tenenbaum, Gérald; Verwee, Johann Effective Erdős-Wintner theorems. (English. Russian original) Zbl 1476.62046 Proc. Steklov Inst. Math. 314, 264-278 (2021); translation from Tr. Mat. Inst. Steklova 314, 275-289 (2021). MSC: 62E20 60E05 11N60 11K65 PDFBibTeX XMLCite \textit{G. Tenenbaum} and \textit{J. Verwee}, Proc. Steklov Inst. Math. 314, 264--278 (2021; Zbl 1476.62046); translation from Tr. Mat. Inst. Steklova 314, 275--289 (2021) Full Text: DOI arXiv
Berkes, István; Borda, Bence On the discrepancy of random subsequences of \(\{n\alpha \}\). II. (English) Zbl 1479.11131 Acta Arith. 199, No. 3, 303-330 (2021). Reviewer: Jean-Paul Allouche (Paris) MSC: 11K38 11K60 60G50 60F17 PDFBibTeX XMLCite \textit{I. Berkes} and \textit{B. Borda}, Acta Arith. 199, No. 3, 303--330 (2021; Zbl 1479.11131) Full Text: arXiv
Taylor-Crush, Toby On the regularity and approximation of invariant densities for random continued fractions. (English) Zbl 1475.37042 Dyn. Syst. 36, No. 1, 1-18 (2021). Reviewer: Steve Pederson (Atlanta) MSC: 37E05 37H12 11A55 PDFBibTeX XMLCite \textit{T. Taylor-Crush}, Dyn. Syst. 36, No. 1, 1--18 (2021; Zbl 1475.37042) Full Text: DOI arXiv
Giuliano, Rita; Hadjikyriakou, Milto Convergence for weighted sums of Lüroth type random variables. (English) Zbl 1470.60076 J. Math. Anal. Appl. 502, No. 2, Article ID 125263, 36 p. (2021). MSC: 60F05 11K55 PDFBibTeX XMLCite \textit{R. Giuliano} and \textit{M. Hadjikyriakou}, J. Math. Anal. Appl. 502, No. 2, Article ID 125263, 36 p. (2021; Zbl 1470.60076) Full Text: DOI arXiv
Shang, Lei; Wu, Min On the growth speed of digits in Engel expansions. (English) Zbl 1459.11164 J. Number Theory 219, 368-385 (2021). Reviewer: Symon Serbenyuk (Kyïv) MSC: 11K55 28A80 PDFBibTeX XMLCite \textit{L. Shang} and \textit{M. Wu}, J. Number Theory 219, 368--385 (2021; Zbl 1459.11164) Full Text: DOI
Rosenblatt, Joseph; Roychowdhury, Mrinal Kanti Optimal quantization via dynamics. (English) Zbl 1466.62239 Dyn. Syst. 35, No. 3, 522-538 (2020). MSC: 62B10 60B05 11J71 37A50 PDFBibTeX XMLCite \textit{J. Rosenblatt} and \textit{M. K. Roychowdhury}, Dyn. Syst. 35, No. 3, 522--538 (2020; Zbl 1466.62239) Full Text: DOI arXiv
Takahasi, Hiroki Large deviations for denominators of continued fractions. (English) Zbl 1470.11209 Nonlinearity 33, No. 11, 5861-5874 (2020). MSC: 11K50 60F10 37D35 37A50 PDFBibTeX XMLCite \textit{H. Takahasi}, Nonlinearity 33, No. 11, 5861--5874 (2020; Zbl 1470.11209) Full Text: DOI arXiv
Lascu, Dan; Sebe, Gabriela Ileana A Gauss-Kuz’min-Lévy theorem for Rényi-type continued fractions. (English) Zbl 1448.11133 Acta Arith. 193, No. 3, 283-292 (2020). Reviewer: Michael M. Pahirya (Mukachevo) MSC: 11J70 60A10 PDFBibTeX XMLCite \textit{D. Lascu} and \textit{G. I. Sebe}, Acta Arith. 193, No. 3, 283--292 (2020; Zbl 1448.11133) Full Text: DOI arXiv
Pratsiovytyi, Mykola; Makarchuk, Oleg; Karvatsky, Dmytro Lebesgue structure of asymmetric Bernoulli convolution based on Jacobsthal-Lucas sequence. (English) Zbl 1447.60074 Random Oper. Stoch. Equ. 28, No. 2, 123-130 (2020). MSC: 60G50 11K55 PDFBibTeX XMLCite \textit{M. Pratsiovytyi} et al., Random Oper. Stoch. Equ. 28, No. 2, 123--130 (2020; Zbl 1447.60074) Full Text: DOI
Shang, Lei; Wu, Min Slow growth rate of the digits in Engel expansions. (English) Zbl 1434.11155 Fractals 28, No. 3, Article ID 2050047, 12 p. (2020). MSC: 11K55 28A80 PDFBibTeX XMLCite \textit{L. Shang} and \textit{M. Wu}, Fractals 28, No. 3, Article ID 2050047, 12 p. (2020; Zbl 1434.11155) Full Text: DOI
Acharya, Ratnadeep Exponential sums of squares of Fourier coefficients of cusp forms. (English) Zbl 1439.11118 Proc. Indian Acad. Sci., Math. Sci. 130, No. 1, Paper No. 24, 7 p. (2020). MSC: 11F30 11L03 PDFBibTeX XMLCite \textit{R. Acharya}, Proc. Indian Acad. Sci., Math. Sci. 130, No. 1, Paper No. 24, 7 p. (2020; Zbl 1439.11118) Full Text: DOI
Mehmetaj, Erblin On the \(r\)-continued fraction expansions of reals. (English) Zbl 1439.11162 J. Number Theory 207, 294-314 (2020). Reviewer: Michael M. Pahirya (Mukachevo) MSC: 11J70 11A55 11K50 37E05 PDFBibTeX XMLCite \textit{E. Mehmetaj}, J. Number Theory 207, 294--314 (2020; Zbl 1439.11162) Full Text: DOI
Rudnick, Zeév; Waxman, Ezra Angles of Gaussian primes. (English) Zbl 1467.11107 Isr. J. Math. 232, No. 1, 159-199 (2019). Reviewer: Shabnam Akhtari (Eugene) MSC: 11R45 11M50 11R42 PDFBibTeX XMLCite \textit{Z. Rudnick} and \textit{E. Waxman}, Isr. J. Math. 232, No. 1, 159--199 (2019; Zbl 1467.11107) Full Text: DOI arXiv
De Koninck, Jean-Marie; Kátai, Imre On the values of the Euler function around shifted primes. (English. French summary) Zbl 1436.11118 Ann. Math. Qué. 43, No. 1, 37-50 (2019). Reviewer: Mehdi Hassani (Zanjan) MSC: 11N60 11N25 26A15 PDFBibTeX XMLCite \textit{J.-M. De Koninck} and \textit{I. Kátai}, Ann. Math. Qué. 43, No. 1, 37--50 (2019; Zbl 1436.11118) Full Text: DOI
Kamieński, Piotr A quantitative version of the theorem on Khintchine’s constant. (English) Zbl 1423.11134 Indag. Math., New Ser. 30, No. 4, 649-668 (2019). Reviewer: Alexey Ustinov (Khabarovsk) MSC: 11K50 60F10 PDFBibTeX XMLCite \textit{P. Kamieński}, Indag. Math., New Ser. 30, No. 4, 649--668 (2019; Zbl 1423.11134) Full Text: DOI arXiv
Erdoğan, M. B.; Shakan, G. Fractal solutions of dispersive partial differential equations on the torus. (English) Zbl 1410.35197 Sel. Math., New Ser. 25, No. 1, Paper No. 11, 26 p. (2019). MSC: 35Q55 11L03 35Q53 35Q35 35R11 28A80 76B15 PDFBibTeX XMLCite \textit{M. B. Erdoğan} and \textit{G. Shakan}, Sel. Math., New Ser. 25, No. 1, Paper No. 11, 26 p. (2019; Zbl 1410.35197) Full Text: DOI arXiv
Abdesselam, Abdelmalek Towards three-dimensional conformal probability. (English) Zbl 1420.81023 \(p\)-Adic Numbers Ultrametric Anal. Appl. 10, No. 4, 233-252 (2018). MSC: 81T40 81T17 81T10 81T70 11K41 PDFBibTeX XMLCite \textit{A. Abdesselam}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 10, No. 4, 233--252 (2018; Zbl 1420.81023) Full Text: DOI arXiv
Sun, Peng A generalization of Gauss-Kuzmin-Lévy theorem. (English) Zbl 1438.11107 Acta Math. Sci., Ser. B, Engl. Ed. 38, No. 3, 965-972 (2018). MSC: 11K50 11J70 37C30 PDFBibTeX XMLCite \textit{P. Sun}, Acta Math. Sci., Ser. B, Engl. Ed. 38, No. 3, 965--972 (2018; Zbl 1438.11107) Full Text: DOI arXiv
Madritsch, Manfred Normal numbers and symbolic dynamics. (English) Zbl 1408.11075 Berthé, Valérie (ed.) et al., Sequences, groups, and number theory. Cham: Birkhäuser. Trends Math., 271-329 (2018). MSC: 11K16 37B10 PDFBibTeX XMLCite \textit{M. Madritsch}, in: Sequences, groups, and number theory. Cham: Birkhäuser. 271--329 (2018; Zbl 1408.11075) Full Text: DOI
Massé, Bruno Modulo 1 limit theorems for autoregressive random variables and their sums. (English) Zbl 1391.60007 Stat. Probab. Lett. 135, 70-75 (2018). MSC: 60B10 11K06 PDFBibTeX XMLCite \textit{B. Massé}, Stat. Probab. Lett. 135, 70--75 (2018; Zbl 1391.60007) Full Text: DOI
Wang, Liuquan; Zhang, Cheng Zeros of the deformed exponential function. (English) Zbl 1392.30004 Adv. Math. 332, 311-348 (2018). MSC: 30C15 41A60 11M36 PDFBibTeX XMLCite \textit{L. Wang} and \textit{C. Zhang}, Adv. Math. 332, 311--348 (2018; Zbl 1392.30004) Full Text: DOI arXiv
Rudnick, Zeév A metric theory of minimal gaps. (English) Zbl 1451.11085 Mathematika 64, No. 3, 628-636 (2018). Reviewer: Christoph Aistleitner (Graz) MSC: 11K06 PDFBibTeX XMLCite \textit{Z. Rudnick}, Mathematika 64, No. 3, 628--636 (2018; Zbl 1451.11085) Full Text: DOI arXiv
Chenavier, Nicolas; Massé, Bruno; Schneider, Dominique Products of random variables and the first digit phenomenon. (English) Zbl 1435.11101 Stochastic Processes Appl. 128, No. 5, 1615-1634 (2018). MSC: 11K06 11A63 60F05 PDFBibTeX XMLCite \textit{N. Chenavier} et al., Stochastic Processes Appl. 128, No. 5, 1615--1634 (2018; Zbl 1435.11101) Full Text: DOI arXiv
Becker, Thealexa; Burt, David; Corcoran, Taylor C.; Greaves-Tunnell, Alec; Iafrate, Joseph R.; Jing, Joy; Miller, Steven J.; Porfilio, Jaclyn D.; Ronan, Ryan; Samranvedhya, Jirapat; Strauch, Frederick W.; Talbut, Blaine Benford’s law and continuous dependent random variables. (English) Zbl 1382.60010 Ann. Phys. 388, 350-381 (2018). MSC: 60A10 11K06 60E10 PDFBibTeX XMLCite \textit{T. Becker} et al., Ann. Phys. 388, 350--381 (2018; Zbl 1382.60010) Full Text: DOI arXiv
Blomer, Valentin; Bourgain, Jean; Radziwiłł, Maksym; Rudnick, Zeév Small gaps in the spectrum of the rectangular billiard. (English. French summary) Zbl 1405.35120 Ann. Sci. Éc. Norm. Supér. (4) 50, No. 5, 1283-1300 (2017). Reviewer: Emre Alkan (Istanbul) MSC: 35P20 11E16 11J04 11B39 11L07 PDFBibTeX XMLCite \textit{V. Blomer} et al., Ann. Sci. Éc. Norm. Supér. (4) 50, No. 5, 1283--1300 (2017; Zbl 1405.35120) Full Text: DOI arXiv Link
Spalding, K.; Veselov, A. P. Lyapunov spectrum of Markov and Euclid trees. (English) Zbl 1432.11071 Nonlinearity 30, No. 12, 4428-4453 (2017). MSC: 11J06 37D25 37E25 PDFBibTeX XMLCite \textit{K. Spalding} and \textit{A. P. Veselov}, Nonlinearity 30, No. 12, 4428--4453 (2017; Zbl 1432.11071) Full Text: DOI arXiv Link
Sydoruk, Liliia; Torbin, Grygoriy On singularity of distribution of random variables with independent symbols of Oppenheim expansions. (English) Zbl 1423.11137 Mod. Stoch., Theory Appl. 4, No. 3, 273-283 (2017). MSC: 11K55 60G30 PDFBibTeX XMLCite \textit{L. Sydoruk} and \textit{G. Torbin}, Mod. Stoch., Theory Appl. 4, No. 3, 273--283 (2017; Zbl 1423.11137) Full Text: DOI arXiv
Wu, Jun; Xie, Jian-Sheng Range-renewal structure in continued fractions. (English) Zbl 1369.37012 Ergodic Theory Dyn. Syst. 37, No. 4, 1323-1344 (2017). Reviewer: Simon Baker (Coventry) MSC: 37A45 11A55 11K55 PDFBibTeX XMLCite \textit{J. Wu} and \textit{J.-S. Xie}, Ergodic Theory Dyn. Syst. 37, No. 4, 1323--1344 (2017; Zbl 1369.37012) Full Text: DOI arXiv
Sebe, Gabriela Ileana A near-optimal solution to the Gauss-Kuzmin-Lévy problem for \(\theta\)-expansions. (English) Zbl 1419.11102 J. Number Theory 171, 43-55 (2017). MSC: 11K50 11J70 37B10 PDFBibTeX XMLCite \textit{G. I. Sebe}, J. Number Theory 171, 43--55 (2017; Zbl 1419.11102) Full Text: DOI
Lebid’, M. V.; Torbin, H. M. Singularity and fine fractal properties of one class of infinite Bernoulli convolutions with essential overlapping. II. (English. Ukrainian original) Zbl 1390.60148 Ukr. Math. J. 67, No. 12, 1884-1899 (2016); translation from Ukr. Mat. Zh. 67, No. 12, 1667-1678 (2015). MSC: 60G30 28A80 26A30 28A78 11K55 PDFBibTeX XMLCite \textit{M. V. Lebid'} and \textit{H. M. Torbin}, Ukr. Math. J. 67, No. 12, 1884--1899 (2016; Zbl 1390.60148); translation from Ukr. Mat. Zh. 67, No. 12, 1667--1678 (2015) Full Text: DOI
Bugeaud, Yann; Moreira, Carlos Gustavo Variations around a metric theorem of Khinchin. (Variations autour d’un théorème métrique de Khintchine.) (French. English summary) Zbl 1369.11055 Bull. Soc. Math. Fr. 144, No. 3, 507-538 (2016). Reviewer: Simon Kristensen (Aarhus) MSC: 11J83 11J04 PDFBibTeX XMLCite \textit{Y. Bugeaud} and \textit{C. G. Moreira}, Bull. Soc. Math. Fr. 144, No. 3, 507--538 (2016; Zbl 1369.11055) Full Text: DOI Link
Hančl, Jaroslav; Haddley, A.; Lertchoosakul, P.; Nair, R. Quantitative metric theory of continued fractions. (English) Zbl 1414.11091 Proc. Indian Acad. Sci., Math. Sci. 126, No. 2, 167-177 (2016). MSC: 11K50 28D99 PDFBibTeX XMLCite \textit{J. Hančl} et al., Proc. Indian Acad. Sci., Math. Sci. 126, No. 2, 167--177 (2016; Zbl 1414.11091) Full Text: DOI
Bazarova, Alina; Berkes, István; Horváth, Lajos On the extremal theory of continued fractions. (English) Zbl 1336.11058 J. Theor. Probab. 29, No. 1, 248-266 (2016). Reviewer: Simon Kristensen (Aarhus) MSC: 11K60 60F05 60G70 PDFBibTeX XMLCite \textit{A. Bazarova} et al., J. Theor. Probab. 29, No. 1, 248--266 (2016; Zbl 1336.11058) Full Text: DOI Link
Fang, Lulu; Wu, Min; Li, Bing Limit theorems related to beta-expansion and continued fraction expansion. (English) Zbl 1408.11076 J. Number Theory 163, 385-405 (2016). MSC: 11K50 11K55 60F05 60F15 PDFBibTeX XMLCite \textit{L. Fang} et al., J. Number Theory 163, 385--405 (2016; Zbl 1408.11076) Full Text: DOI arXiv
Bengoechea, Paloma; Zorin, Evgeniy On the mixed Littlewood conjecture and continued fractions in quadratic fields. (English) Zbl 1402.11100 J. Number Theory 162, 1-10 (2016). MSC: 11J13 11J61 11J68 11J70 PDFBibTeX XMLCite \textit{P. Bengoechea} and \textit{E. Zorin}, J. Number Theory 162, 1--10 (2016; Zbl 1402.11100) Full Text: DOI arXiv
Prats’ovytyĭ, M. V.; Savchenko, I. O. The distributions of random incomplete sums of a series with positive terms satisfying the property of non-linear homogeneity. (English. Ukrainian original) Zbl 1346.60053 Theory Probab. Math. Stat. 91, 145-155 (2015); translation from Teor. Jmovirn. Mat. Stat. 91, 133-142 (2014). MSC: 60G30 60G50 28A78 28A80 11K55 PDFBibTeX XMLCite \textit{M. V. Prats'ovytyĭ} and \textit{I. O. Savchenko}, Theory Probab. Math. Stat. 91, 145--155 (2015; Zbl 1346.60053); translation from Teor. Jmovirn. Mat. Stat. 91, 133--142 (2014) Full Text: DOI
Giuliano, Rita; Macci, Claudio Asymptotic results for weighted means of random variables which converge to a Dickman distribution, and some number theoretical applications. (English) Zbl 1333.60031 ESAIM, Probab. Stat. 19, 395-413 (2015). MSC: 60F05 60F10 60F15 11K99 PDFBibTeX XMLCite \textit{R. Giuliano} and \textit{C. Macci}, ESAIM, Probab. Stat. 19, 395--413 (2015; Zbl 1333.60031) Full Text: DOI
Bugeaud, Yann Quadratic approximation to automatic continued fractions. (English. French summary) Zbl 1387.11051 J. Théor. Nombres Bordx. 27, No. 2, 463-482 (2015). MSC: 11J70 11J82 PDFBibTeX XMLCite \textit{Y. Bugeaud}, J. Théor. Nombres Bordx. 27, No. 2, 463--482 (2015; Zbl 1387.11051) Full Text: DOI Numdam
Dajani, Karma; Kraaikamp, Cor; Langeveld, Niels Daniël Simon Continued fraction expansions with variable numerators. (English) Zbl 1321.28028 Ramanujan J. 37, No. 3, 617-639 (2015). MSC: 28D05 11K50 PDFBibTeX XMLCite \textit{K. Dajani} et al., Ramanujan J. 37, No. 3, 617--639 (2015; Zbl 1321.28028) Full Text: DOI Link
Berthé, Valérie; Cesaratto, Eda; Rotondo, Pablo; Vallée, Brigitte; Viola, Alfredo Recurrence function on Sturmian words: a probabilistic study. (English) Zbl 1465.68220 Italiano, F. (ed.) et al., Mathematical foundations of computer science 2015. 40th international symposium, MFCS 2015, Milan, Italy, August 24–28, 2015. Proceedings. Part I. Berlin: Springer. Lect. Notes Comput. Sci. 9234, 116-128 (2015). MSC: 68R15 05A05 11B37 60C05 PDFBibTeX XMLCite \textit{V. Berthé} et al., Lect. Notes Comput. Sci. 9234, 116--128 (2015; Zbl 1465.68220) Full Text: DOI
Behrends, Ehrhard From shuffling cards to Artin’s conjecture. (Vom Kartenmischen zur Artinvermutung.) (German) Zbl 1336.11003 Math. Semesterber. 62, No. 1, 7-15 (2015). MSC: 11A07 11B75 00A08 PDFBibTeX XMLCite \textit{E. Behrends}, Math. Semesterber. 62, No. 1, 7--15 (2015; Zbl 1336.11003) Full Text: DOI
Fang, Lulu; Wu, Min; Shieh, Narn-Rueih; Li, Bing Random continued fractions: Lévy constant and Chernoff-type estimate. (English) Zbl 1322.11011 J. Math. Anal. Appl. 429, No. 1, 513-531 (2015). Reviewer: Yuliya S. Mishura (Kyïv) MSC: 11A55 11J70 11K50 40A15 60G51 60F15 60G10 PDFBibTeX XMLCite \textit{L. Fang} et al., J. Math. Anal. Appl. 429, No. 1, 513--531 (2015; Zbl 1322.11011) Full Text: DOI arXiv
Hu, Wei Moderate deviation principles for Engel’s, Sylvester’s series and Cantor’s products. (English) Zbl 1335.60051 Stat. Probab. Lett. 96, 247-254 (2015). MSC: 60F10 11A67 PDFBibTeX XMLCite \textit{W. Hu}, Stat. Probab. Lett. 96, 247--254 (2015; Zbl 1335.60051) Full Text: DOI
Indlekofer, Karl-Heinz On a conjecture of Erdős about additive functions. (English) Zbl 1361.11058 Theory Probab. Math. Stat. 89, 23-31 (2014); translation from Teor. Jmovirn. Mat. Stat. 89, 21–29 (2013). MSC: 11N37 11N60 11K65 PDFBibTeX XMLCite \textit{K.-H. Indlekofer}, Theory Probab. Math. Stat. 89, 23--31 (2014; Zbl 1361.11058); translation from Teor. Jmovirn. Mat. Stat. 89, 21--29 (2013) Full Text: DOI
Glöckner, Helge; Lucht, Lutz G. Weighted inversion of general Dirichlet series. (English) Zbl 1295.11095 Trans. Am. Math. Soc. 366, No. 6, 3275-3293 (2014). Reviewer: Maciej Radziejewski (Poznań) MSC: 11M41 30B50 30J99 46H99 PDFBibTeX XMLCite \textit{H. Glöckner} and \textit{L. G. Lucht}, Trans. Am. Math. Soc. 366, No. 6, 3275--3293 (2014; Zbl 1295.11095) Full Text: DOI arXiv
Sebe, Gabriela Ileana; Lascu, Dan A Gauss-Kuzmin theorem and related questions for \(\theta \)-expansions. (English) Zbl 1291.11106 J. Funct. Spaces 2014, Article ID 980461, 12 p. (2014). Reviewer: Michael M. Pahirya (Mukachevo) MSC: 11K50 11A55 11J70 40A15 PDFBibTeX XMLCite \textit{G. I. Sebe} and \textit{D. Lascu}, J. Funct. Spaces 2014, Article ID 980461, 12 p. (2014; Zbl 1291.11106) Full Text: DOI arXiv
Lascu, Dan A Gauss-Kuzmin-type problem for a family of continued fraction expansions. (English) Zbl 1319.11049 J. Number Theory 133, No. 7, 2153-2181 (2013). Reviewer: Chryssoula Ganatsiou (Larissa) MSC: 11K50 37A45 37A50 PDFBibTeX XMLCite \textit{D. Lascu}, J. Number Theory 133, No. 7, 2153--2181 (2013; Zbl 1319.11049) Full Text: DOI arXiv
Moree, Pieter Moser’s mathemagical work on the equation \(1^k+2^k+\ldots+(m-1)^k=m^k\). (English) Zbl 1362.11045 Rocky Mt. J. Math. 43, No. 5, 1707-1737 (2013). MSC: 11D61 11A07 PDFBibTeX XMLCite \textit{P. Moree}, Rocky Mt. J. Math. 43, No. 5, 1707--1737 (2013; Zbl 1362.11045) Full Text: DOI arXiv Euclid
Ustinov, A. V. Spin chains and Arnold’s problem on the Gauss-Kuz’min statistics for quadratic irrationals. (English. Russian original) Zbl 1288.11092 Sb. Math. 204, No. 5, 762-779 (2013); translation from Mat. Sb. 204, No. 5, 143-160 (2013). Reviewer: Dmitriy Frolenkov (Moscow) MSC: 11N37 11L07 11K50 11A55 PDFBibTeX XMLCite \textit{A. V. Ustinov}, Sb. Math. 204, No. 5, 762--779 (2013; Zbl 1288.11092); translation from Mat. Sb. 204, No. 5, 143--160 (2013) Full Text: DOI Link
Gallot, Yves; Moree, Pieter; Zudilin, Wadim The Erdős–Moser equation \(1^k+2^k+\cdots +(m-1)^k=m^k\) revisited using continued fractions. (English) Zbl 1231.11038 Math. Comput. 80, No. 274, 1221-1237 (2011). Reviewer: Kálmán Liptai (Eger) MSC: 11D61 11Y65 11A55 PDFBibTeX XMLCite \textit{Y. Gallot} et al., Math. Comput. 80, No. 274, 1221--1237 (2011; Zbl 1231.11038) Full Text: DOI arXiv
Szewczak, Zbigniew S. A local limit theorem for continued fractions. (English) Zbl 1209.60022 Stoch. Dyn. 10, No. 3, 429-439 (2010). Reviewer: Tae Il. Jeon (Taejon) MSC: 60F99 11K50 PDFBibTeX XMLCite \textit{Z. S. Szewczak}, Stoch. Dyn. 10, No. 3, 429--439 (2010; Zbl 1209.60022) Full Text: DOI
Szewczak, Zbigniew S. A limit theorem for random sums modulo 1. (English) Zbl 1196.60057 Stat. Probab. Lett. 80, No. 9-10, 747-751 (2010). Reviewer: Marius Iosifescu (Bucureşti) MSC: 60F99 60J10 11K06 PDFBibTeX XMLCite \textit{Z. S. Szewczak}, Stat. Probab. Lett. 80, No. 9--10, 747--751 (2010; Zbl 1196.60057) Full Text: DOI
Baxa, Christoph Lévy constants of transcendental numbers. (English) Zbl 1179.11020 Proc. Am. Math. Soc. 137, No. 7, 2243-2249 (2009). Reviewer: Simon Kristensen (Aarhus) MSC: 11J81 11J82 PDFBibTeX XMLCite \textit{C. Baxa}, Proc. Am. Math. Soc. 137, No. 7, 2243--2249 (2009; Zbl 1179.11020) Full Text: DOI
Li, Bing; Wu, Jun Beta-expansion and continued fraction expansion over formal Laurent series. (English) Zbl 1165.11066 Finite Fields Appl. 14, No. 3, 635-647 (2008). Reviewer: Simon Kristensen (Aarhus) MSC: 11K55 11K50 11J61 PDFBibTeX XMLCite \textit{B. Li} and \textit{J. Wu}, Finite Fields Appl. 14, No. 3, 635--647 (2008; Zbl 1165.11066) Full Text: DOI
Wang, Baowei; Wu, Jun Hausdorff dimension of certain sets arising in continued fraction expansions. (English) Zbl 1233.11084 Adv. Math. 218, No. 5, 1319-1339 (2008). MSC: 11K50 11K55 28A78 28A80 PDFBibTeX XMLCite \textit{B. Wang} and \textit{J. Wu}, Adv. Math. 218, No. 5, 1319--1339 (2008; Zbl 1233.11084) Full Text: DOI
Li, Bing; Wu, Jun Beta-expansion and continued fraction expansion. (English) Zbl 1137.11053 J. Math. Anal. Appl. 339, No. 2, 1322-1331 (2008). Reviewer: Simon Kristensen (Aarhus) MSC: 11K55 11K50 PDFBibTeX XMLCite \textit{B. Li} and \textit{J. Wu}, J. Math. Anal. Appl. 339, No. 2, 1322--1331 (2008; Zbl 1137.11053) Full Text: DOI
Karpenkov, O. N. On an invariant Möbius measure and the Gauss-Kuzmin face distribution. (English. Russian original) Zbl 1245.52006 Proc. Steklov Inst. Math. 258, 74-86 (2007); translation from Tr. Mat. Inst. Steklova 258, 79-92 (2007). MSC: 52C07 11A55 52A20 PDFBibTeX XMLCite \textit{O. N. Karpenkov}, Proc. Steklov Inst. Math. 258, 74--86 (2007; Zbl 1245.52006); translation from Tr. Mat. Inst. Steklova 258, 79--92 (2007) Full Text: DOI
de Haan, R.; Jacobson, M. J. jun.; Williams, H. C. A fast, rigorous technique for computing the regulator of a real quadratic field. (English) Zbl 1126.11072 Math. Comput. 76, No. 260, 2139-2160 (2007). MSC: 11Y40 11Y16 PDFBibTeX XMLCite \textit{R. de Haan} et al., Math. Comput. 76, No. 260, 2139--2160 (2007; Zbl 1126.11072) Full Text: DOI
Nathanson, Melvyn B.; Parikh, Rohit Density of sets of natural numbers and the Lévy group. (English) Zbl 1128.11006 J. Number Theory 124, No. 1, 151-158 (2007). Reviewer: Štefan Porubský (Praha) MSC: 11B05 11B13 11B75 PDFBibTeX XMLCite \textit{M. B. Nathanson} and \textit{R. Parikh}, J. Number Theory 124, No. 1, 151--158 (2007; Zbl 1128.11006) Full Text: DOI arXiv
Wu, Jun Continued fraction and decimal expansions of an irrational number. (English) Zbl 1156.11033 Adv. Math. 206, No. 2, 684-694 (2006). Reviewer: Jean-Paul Allouche (Orsay) MSC: 11K50 11K16 11K55 PDFBibTeX XMLCite \textit{J. Wu}, Adv. Math. 206, No. 2, 684--694 (2006; Zbl 1156.11033) Full Text: DOI
Baladi, Viviane; Vallée, Brigitte Euclidean algorithms are Gaussian. (English) Zbl 1114.11092 J. Number Theory 110, No. 2, 331-386 (2005). MSC: 11Y16 37A45 37C30 60F05 68W40 PDFBibTeX XMLCite \textit{V. Baladi} and \textit{B. Vallée}, J. Number Theory 110, No. 2, 331--386 (2005; Zbl 1114.11092) Full Text: DOI
Barbolosi, D.; Faivre, C. On the large partial quotients in the continued fraction expansion. (Sur les grands quotients partiels du développement en fraction continue.) (French) Zbl 1057.11037 J. Number Theory 106, No. 2, 299-325 (2004). Reviewer: Valérie Berthé (Montpellier) MSC: 11K50 11A55 PDFBibTeX XMLCite \textit{D. Barbolosi} and \textit{C. Faivre}, J. Number Theory 106, No. 2, 299--325 (2004; Zbl 1057.11037) Full Text: DOI
Marcolli, Matilde Limiting modular symbols and the Lyapunov spectrum. (English) Zbl 1158.11316 J. Number Theory 98, No. 2, 348-376 (2003). Reviewer: Paula Tretkoff (MR1955422) MSC: 11F67 11M36 37C30 PDFBibTeX XMLCite \textit{M. Marcolli}, J. Number Theory 98, No. 2, 348--376 (2003; Zbl 1158.11316) Full Text: DOI arXiv
Hartono, Yusuf; Kraaikamp, Cor; Schweiger, Fritz Algebraic and ergodic properties of a new continued fraction algorithm with non-decreasing partial quotients. (English) Zbl 1067.11042 J. Théor. Nombres Bordx. 14, No. 2, 497-516 (2002). Reviewer: Takao Komatsu (Hirosaki) MSC: 11K50 37A45 PDFBibTeX XMLCite \textit{Y. Hartono} et al., J. Théor. Nombres Bordx. 14, No. 2, 497--516 (2002; Zbl 1067.11042) Full Text: DOI Numdam EuDML
Allouche, J.-P.; Davison, J. L.; Queffélec, M.; Zamboni, L. Q. Transcendence of Sturmian or morphic continued fractions. (English) Zbl 0998.11036 J. Number Theory 91, No. 1, 39-66 (2001). Reviewer: R.F.Tichy (Graz) MSC: 11J70 11B83 PDFBibTeX XMLCite \textit{J. P. Allouche} et al., J. Number Theory 91, No. 1, 39--66 (2001; Zbl 0998.11036) Full Text: DOI Link
Biane, Philippe; Pitman, Jim; Yor, Marc Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions. (English) Zbl 1040.11061 Bull. Am. Math. Soc., New Ser. 38, No. 4, 435-465 (2001). Reviewer: Emilio Elizalde (Barcelona) MSC: 11M06 60J65 60E07 PDFBibTeX XMLCite \textit{P. Biane} et al., Bull. Am. Math. Soc., New Ser. 38, No. 4, 435--465 (2001; Zbl 1040.11061) Full Text: DOI arXiv
Heinrich, L. On the asymptotic behaviour of the integral \(\int_0^\infty e^{itx}\left(\frac{1}{x^\alpha}-\frac{1}{[x^\alpha]+1}\right)dx (t\to 0)\) and rates of convergence to \(\alpha\)-stable limit laws. (English) Zbl 0985.41022 Z. Anal. Anwend. 20, No. 2, 379-394 (2001). Reviewer: J.M.Rappoport MSC: 41A60 40E05 11K50 60E07 PDFBibTeX XMLCite \textit{L. Heinrich}, Z. Anal. Anwend. 20, No. 2, 379--394 (2001; Zbl 0985.41022) Full Text: DOI
Vallée, Brigitte Digits and continuants in Euclidean algorithms. Ergodic versus Tauberian theorems. (English) Zbl 0973.11079 J. Théor. Nombres Bordx. 12, No. 2, 531-570 (2000). Reviewer: Jean-Paul Allouche (Orsay) MSC: 11K99 68W40 11K50 11K55 68Q25 37A45 11M99 11Y65 PDFBibTeX XMLCite \textit{B. Vallée}, J. Théor. Nombres Bordx. 12, No. 2, 531--570 (2000; Zbl 0973.11079) Full Text: DOI Numdam EuDML EMIS
Dajani, Karma; Kraaikamp, Cor A Gauss-Kusmin theorem for optimal continued fractions. (English) Zbl 0921.11040 Trans. Am. Math. Soc. 351, No. 5, 2055-2079 (1999). Reviewer: Takao Komatsu (Tsu) MSC: 11K50 28D05 PDFBibTeX XMLCite \textit{K. Dajani} and \textit{C. Kraaikamp}, Trans. Am. Math. Soc. 351, No. 5, 2055--2079 (1999; Zbl 0921.11040) Full Text: DOI
Faivre, C. The rate of convergence of approximations of a continued fraction. (English) Zbl 0909.11031 J. Number Theory 68, No. 1, 21-28 (1998). Reviewer: S.L.Kalpazidou (Thessaloniki) MSC: 11K50 PDFBibTeX XMLCite \textit{C. Faivre}, J. Number Theory 68, No. 1, 21--28 (1998; Zbl 0909.11031) Full Text: DOI
Faivre, C. The Lévy constant of an irrational number. (English) Zbl 0923.11020 Acta Math. Hung. 74, No. 1-2, 57-61 (1997). MSC: 11A55 PDFBibTeX XMLCite \textit{C. Faivre}, Acta Math. Hung. 74, No. 1--2, 57--61 (1997; Zbl 0923.11020) Full Text: DOI
Samur, Jorge D. Some remarks on a probability limit theorem for continued fractions. (English) Zbl 0863.11048 Trans. Am. Math. Soc. 348, No. 4, 1411-1428 (1996). Reviewer: L.Heinrich (Freiberg) MSC: 11K50 60F17 11K60 PDFBibTeX XMLCite \textit{J. D. Samur}, Trans. Am. Math. Soc. 348, No. 4, 1411--1428 (1996; Zbl 0863.11048) Full Text: DOI
Broise, Anne Multidimensional continued fractions and stable laws. (Fractions continues multidimensionnelles et lois stables.) (French) Zbl 0857.11035 Bull. Soc. Math. Fr. 124, No. 1, 97-139 (1996). Reviewer: Ph.Biane (Paris) MSC: 11J70 37A99 60F05 PDFBibTeX XMLCite \textit{A. Broise}, Bull. Soc. Math. Fr. 124, No. 1, 97--139 (1996; Zbl 0857.11035) Full Text: DOI Numdam EuDML Link
Shiu, P. Computation of continued fractions without input values. (English) Zbl 0834.11004 Math. Comput. 64, No. 211, 1307-1317 (1995). Reviewer: H.J.Godwin (Egham) MSC: 11A55 11Y65 11K50 PDFBibTeX XMLCite \textit{P. Shiu}, Math. Comput. 64, No. 211, 1307--1317 (1995; Zbl 0834.11004) Full Text: DOI
Dajani, Karma; Kraaikamp, Cor Generalization of a theorem of Kusmin. (English) Zbl 0819.11028 Monatsh. Math. 118, No. 1-2, 55-73 (1994). Reviewer: P.Szüsz (Glen/NH) MSC: 11K55 28D05 PDFBibTeX XMLCite \textit{K. Dajani} and \textit{C. Kraaikamp}, Monatsh. Math. 118, No. 1--2, 55--73 (1994; Zbl 0819.11028) Full Text: DOI EuDML
Nair, R. On the metrical theory of continued fractions. (English) Zbl 0796.11031 Proc. Am. Math. Soc. 120, No. 4, 1041-1046 (1994). Reviewer: G.Larcher (Salzburg) MSC: 11K50 28D99 PDFBibTeX XMLCite \textit{R. Nair}, Proc. Am. Math. Soc. 120, No. 4, 1041--1046 (1994; Zbl 0796.11031) Full Text: DOI
Arnoux, Pierre; Nogueira, Arnaldo Gauss measures for multidimensional continued fraction algorithms. (Mesures de Gauss pour des algorithmes de fractions continues multidimensionnelles.) (French) Zbl 0801.11036 Ann. Sci. Éc. Norm. Supér. (4) 26, No. 6, 645-664 (1993). Reviewer: S.L.Kalpazidou (Thessaloniki) MSC: 11K55 28D05 PDFBibTeX XMLCite \textit{P. Arnoux} and \textit{A. Nogueira}, Ann. Sci. Éc. Norm. Supér. (4) 26, No. 6, 645--664 (1993; Zbl 0801.11036) Full Text: DOI Numdam EuDML
Mauclaire, Jean-Loup On the distribution of \(q\)-additive functions. (Sur la répartition des fonctions \(q\)-additives.) (French) Zbl 0788.11032 J. Théor. Nombres Bordx. 5, No. 1, 79-91 (1993). Reviewer: I.Z.Ruzsa (Budapest) MSC: 11K65 PDFBibTeX XMLCite \textit{J.-L. Mauclaire}, J. Théor. Nombres Bordx. 5, No. 1, 79--91 (1993; Zbl 0788.11032) Full Text: DOI Numdam EuDML
Durner, Alexander On a theorem of Gauss-Kuzmin-Lévy. (English) Zbl 0748.11036 Arch. Math. 58, No. 3, 251-256 (1992). Reviewer: A.Durner (Stuttgart) MSC: 11K50 PDFBibTeX XMLCite \textit{A. Durner}, Arch. Math. 58, No. 3, 251--256 (1992; Zbl 0748.11036) Full Text: DOI
Blümlinger, M.; Obata, N. Permutations preserving Cesàro mean, densities of natural numbers and uniform distribution of sequences. (English) Zbl 0735.11004 Ann. Inst. Fourier 41, No. 3, 665-678 (1991). MSC: 11B05 11K06 40G05 20B27 PDFBibTeX XMLCite \textit{M. Blümlinger} and \textit{N. Obata}, Ann. Inst. Fourier 41, No. 3, 665--678 (1991; Zbl 0735.11004) Full Text: DOI Numdam EuDML
Samur, Jorge D. On some limit theorems for continued fractions. (English) Zbl 0676.60015 Trans. Am. Math. Soc. 316, No. 1, 53-79 (1989). Reviewer: R.J.Tomkins MSC: 60E05 60F17 11K60 60F05 11K16 60B12 26A12 PDFBibTeX XMLCite \textit{J. D. Samur}, Trans. Am. Math. Soc. 316, No. 1, 53--79 (1989; Zbl 0676.60015) Full Text: DOI
Philipp, Walter Limit theorems for sums of partial quotients of continued fractions. (English) Zbl 0638.60039 Monatsh. Math. 105, No. 3, 195-206 (1988). Reviewer: W.Philipp MSC: 60F15 11K50 60F05 PDFBibTeX XMLCite \textit{W. Philipp}, Monatsh. Math. 105, No. 3, 195--206 (1988; Zbl 0638.60039) Full Text: DOI EuDML
Mayer, D.; Roepstorff, G. On the relaxation time of Gauss’ continued-fraction map. I: The Hilbert space approach (Koopmanism). (English) Zbl 0658.10057 J. Stat. Phys. 47, No. 1-2, 149-171 (1987). MSC: 11K16 37A99 47B10 28D05 82B99 PDFBibTeX XMLCite \textit{D. Mayer} and \textit{G. Roepstorff}, J. Stat. Phys. 47, No. 1--2, 149--171 (1987; Zbl 0658.10057) Full Text: DOI
Knuth, Donald E. The distribution of continued fraction approximations. (English) Zbl 0547.10030 J. Number Theory 19, 443-448 (1984). Reviewer: H.Jager MSC: 11J70 11K16 PDFBibTeX XMLCite \textit{D. E. Knuth}, J. Number Theory 19, 443--448 (1984; Zbl 0547.10030) Full Text: DOI
Szüsz, P. On the law of iterated logarithm for continued fractions. (English) Zbl 0206.19401 Z. Wahrscheinlichkeitstheor. Verw. Geb. 19, 167-171 (1971). MSC: 60F99 11A55 PDFBibTeX XMLCite \textit{P. Szüsz}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 19, 167--171 (1971; Zbl 0206.19401) Full Text: DOI
Galambos, Janos Distribution of arithmetical functions. A survey. (English) Zbl 0209.34901 Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. B 6, 281-305 (1970). MSC: 11N60 PDFBibTeX XMLCite \textit{J. Galambos}, Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. B 6, 281--305 (1970; Zbl 0209.34901) Full Text: Numdam EuDML
Dixon, J. D. The number of steps in the Euclidean algorithm. (English) Zbl 0206.33502 J. Number Theory 2, 414-422 (1970). MSC: 11A05 PDFBibTeX XMLCite \textit{J. D. Dixon}, J. Number Theory 2, 414--422 (1970; Zbl 0206.33502) Full Text: DOI
Philipp, W.; Stackelberg, O. P. Zwei Grenzwertsätze für Kettenbrüche. (German) Zbl 0164.05602 Math. Ann. 181, 152-156 (1969). Reviewer: Walter Philipp MSC: 11K50 60F99 PDFBibTeX XMLCite \textit{W. Philipp} and \textit{O. P. Stackelberg}, Math. Ann. 181, 152--156 (1969; Zbl 0164.05602) Full Text: DOI EuDML