User:Charles R Greathouse IV/Base

Research papers

This is a collection of papers doing particularly deep, difficult, or applicable work in base-dependent mathematics (particularly as it pertains to integer sequences).

• C. Heuberger and D. Krenn, Asymptotic Analysis of Regular Sequences, Algorithmica 82 (2020), pp. 429-508. arXiv:1810.13178 [math.CO]
• S. K. Jakobsen and J. G. Simonsen, Liouville numbers and the computational complexity of changing bases (2020). In: Marcella Anselmo, Gianluca Della Vedova, Florin Manea, and Arno Pauly (eds), Beyond the Horizon of Computability. CiE 2020. Lecture Notes in Computer Science, vol 12098. Springer, Cham.
• Bryce Kerr, László Mérai, and Igor E. Shparlinski, On digits of Mersenne numbers (2020 preprint). arXiv:2001.03380 [math.NT]
• Kyle Pratt, Primes from sums of two squares and missing digits, Proceedings of the London Mathematical Society 3:120 (2020), pp. 770–830. arXiv:1806.02699 [math.NT]
• James Maynard, Primes with restricted digits, Inventiones mathematicae 217:1 (2019), pp. 127–218.
• L. Mérai and A. Winterhof, On the pseudorandomness of automatic sequences, Cryptography and Communications 10 (2018), pp. 1013–1022. arXiv:1710.03026 [math.NT]
• Robert J. Lemke Oliver and Kannan Soundararajan, The distribution of consecutive prime biases and sums of sawtooth random variables, Mathematical Proceedings of the Cambridge Philosophical Society 168:1(2018), pp. 1–21. arXiv:1709.06168 [math.NT]
• Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit, The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations (2017 preprint), arXiv:1707.03894 [math.NT]
• Robert J. Lemke Oliver and Kannan Soundararajan, Unexpected biases in the distribution of consecutive primes, Proceedings of the National Academy of Sciences 113:31 (2016), E4446-E4454. arXiv:1603.03720 [math.NT]
• Jean Bourgain, Prescribing the binary digits of primes, II, Israel Journal of Mathematics 206:1 (2014), pp. 165–182.
• Jean Bourgain, Prescribing the binary digits of primes, Israel Journal of Mathematics 194:2 (2013), pp. 935–955. arXiv:1105.3895 [math.NT]
• Terence Tao, A remark on primality testing and decimal expansions, Journal of the Australian Mathematical Society 91:3 (2011), pp. 405–413. arXiv:0802.3361 [math.NT]
• Michael Drmota, Christian Mauduit, and Joël Rivat, The sum‐of‐digits function of polynomial sequences, Journal of the London Mathematical Society 84:1 (2011), pp. 81–102.
• Christian Mauduit and Joël Rivat, Sur un problème de Gelfond : la somme des chiffres des nombres premiers, Annals of Mathematics 171:3 (2010), pp. 1591–1646.
• Michael Drmota, Christian Mauduit, and Joël Rivat, Primes with an average sum of digits, Compositio Mathematica 145:2 (2009), pp. 271–292.
• Michael Drmota, Joël Rivat, and Thomas Stoll, The sum of digits of primes in ℤ[i], Monatshefte für Mathematik 155:3–4 (2008), pp. 317–347.
• M. P. Drazin and J. Stanley Griffith, On the decimal representation of integers, Mathematical Proceedings of the Cambridge Philosophical Society 48:4 (October 1952), pp. 555–565.

Surveys and Monographs

This is a list of serious surveys of material related to base-dependent mathematics (particularly as it pertains to integer sequences).

• Louis H. Y. Chen, Hsien-Kuei Hwang, and Vytas Zacharovas, Distribution of the sum-of-digits function of random integers: A survey, Probability Surveys 11 (2014), 60 pp.
• Jean-Paul Allouche and Jeffrey Shallit, Automatic Sequences: Theory, Applications, Generalizations, Cambridge University Press, 2003.