Keywords and phrases: prime number, ova-angular rotation, geometric properties, Dirichlet’s theorem.
Received: April 28, 2021; Accepted: August 24, 2021; Published: September 1, 2021
How to cite this article: Yeisson Alexis Acevedo Agudelo, Prime numbers: an alternative study using ova-angular rotations, JP Journal of Algebra, Number Theory and Applications 52(1) (2021), 127-161. DOI: 10.17654/NT052010127
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] A. Vatwani, Bounded gaps between Gaussian primes, J. Number Theory 171 (2017), 449-473. doi: 10.1016/j.jnt.2016.07.008. [2] M. R. Murty and A. Vatwani, Twin primes and the parity problem, J. Number Theory 180 (2017), 643-659. doi:10.1016/j.jnt.2017.05.011. [3] J. Avigad and R. Morris, The concept of “character” in Dirichlet’s theorem on primes in an arithmetic progression, Arch. Hist. Exact Sci. 68 (2014), 265-326. doi:10.1007/s00407-013-0126-0. [4] S.-C. Chen, Congruences for t-core partition functions, J. Number Theory 133(12) (2013), 4036-4046. doi:10.1016/j.jnt.2013.06.003. [5] T. Tao, Every odd number greater than 1 is the sum of at most five primes, Math. Comp. 83(286) (2014), 997-1038. arXiv:1201.6656v4, doi:10.1090/S0025-5718-2013-02733-0. [6] K. Matomäki, M. Radziwiłł and T. Tao, Correlations of the Von Mangoldt and higher divisor functions I. Long shift ranges, Proc. Lond. Math. Soc. 118 (2018), 284-350. arXiv:1707.01315, doi:10.1112/plms.12181. [7] Z. Tianshu, There are infinitely many sets of N-odd prime numbers and pairs of consecutive odd prime numbers, Advances in Theoretical and Applied Mathematics 8(1) (2013), 17-26. [8] A. Breitzman, Major milestones in twin prime conjecture, Math. Sci. 41 (2016), 3-15. [9] Kenneth H. Rosen, Elementary Number Theory and its Applications, 6th ed., Monmouth University, 2011. [10] Y. Acevedo and L. Cataño, Capitulo especial: Física y su relación de constitución con la matemática, en Campo Magnético, 1st ed., Vol. I, Académica Española, 2017. [11] Y. D. Sergeyev, Numerical Computations with Infinite and Infinitesimal Numbers: Theory and Applications, 1st ed., Vol. I, Springer, 2013. [12] H. Naruse, Elementary proof and application of the generating functions for generalized Hall-Littlewood functions, J. Algebra 516 (2018), 197-209. doi:https://doi.org/10.1016/j.jalgebra.2018.09.010. [13] Stephan Baier and Liangyi Zhao, On primes in quadratic progressions, Int. J. Number Theory 5 (2009), 1017-1035. [14] P. Kuhn, Uber die primteiler eines polynoms, Proceedings of the International Congress of Mathematicians 2 (1954), 35-37. [15] H. Helfgot, Major arcs for Goldbach problem, 2014. arXiv:1305.2897. [16] Y. Acevedo, A complete classification of the Mersenne’s primes and its implications for computing, Revista Politécnica 16(32) (2020), 111-119. doi:https://doi.org/10.33571/rpolitec.v16n32a10. [17] K. Soundararajan, Small gaps between prime numbers: the work of Goldston-Pintz-Yıldırım, Bull. Amer. Math. Soc. (N.S.) 44 (2007), 1-18. http://www.ams.org/journals/bull/2007-44-01/S0273-0979-06-01142-6/S0273-0979-06-01142-6.pdf. [18] D. A. Goldston, S. W. Graham, A. Panidapu, J. Pintz, J. Schettler and C. Y. Yildirim, Small gaps between almost primes, the parity problem, and some conjectures of Erdős on consecutive integers II, J. Number Theory 221 (2021), 222-231. doi:https://doi.org/10.1016/j.jnt.2020.06.002.
|