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© Centre for Modeling & Simulation, Savitribai Phule Pune University
| Title | Biases in prime factorizations and Liouville functions for arithmetic progressions |
| Author/s |
Peter Humphries
University College London, London WC1E 6BT, United Kingdom Snehal M. Shekatkar Centre for Modeling and Simulation, Savitribai Phule Pune University, Pune 411 007 India Tian An Wong Smith College, Northampton06013 MA, USA |
| Abstract | We introduce a refinement of the classical Liouville function to primes in arithmetic progressions. Using this, we show that the occurrence of primes in the prime factorizations of integers depends on the arithmetic progressions to which the given primes belong. Supported by numerical tests, we are led to consider analogues of Pólya’s conjecture, and prove results related to the sign changes of the associated summatory functions. |
| Keywords | Liouville function, prime factorization, arithmetic progressions, Applied Mathematics |
| Download | Journal |
| Citing This Document | Peter Humphries, Snehal M. Shekatkar, and Tian An Wong, Biases in prime factorizations and Liouville functions for arithmetic progressions. Technical Report CMS-TR-20180918 of the Centre for Modeling and Simulation, Savitribai Phule Pune University, Pune 411007, India (2018); available at http://cms.unipune.ac.in/reports/. |
| Notes, Published Reference, Etc. | |
| Contact | snehal.shekatkar@cms.unipune.ac.in |
| Supplementary Material |