On the Polynomial Structure of rk(n)
Main Article Content
Abstract
If rk(n) is the number of representations of a positive integer n as the sum of k squares, then rk(n) is a polynomial in k of degree n; here we exhibit expressions for certain coefficients through this polynomial.
Downloads
Article Details

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
How to Cite
References
G. E. Andrews, S. Kumar Jha, J. López-Bonilla, Sums of squares, triangular numbers, and divisor sums, J. of Integer Sequences 26 (2023) Article 23.2.5
E. Grosswald, Representations of integers as sums of squares, Springer-Verlag, New York (1985).
C. J. Moreno, S. S. Wagstaff Jr, Sums of squares of integers, Chapman & Hall / CRC, Boca Raton, Fl, USA (2006).
M. Aka, M. Einsiedler, T. Ward, A journey through the realm of numbers, Springer, Switzerland (2020).
J. López-Bonilla, J. Yaljá Montiel-Pérez, H. Sherzad Taher, Recurrence relations and Jacobi theta functions, J. de Ciencia e Ingeniería 15, No. 1 (2023) 14-|16. https://oeis.org/
Prof. Michael Somos, Private communication, 1th July 2023.
R. Sivaramakrishnan, Classical theory of arithmetic functions, Marcel Dekker, New York (1989).
G. Everest, T. Ward, An introduction to number theory, Springer-Verlag, London (2005).
R. Sivaraman, J. D. Bulnes, J. López-Bonilla, Sum of divisors function, Int. J. of Maths. and Computer Res. 11, No. 7 (2023) 3540-3542.
A. Hernández-Galeana, M. Muniru Iddrisu, J. López-Bonilla,A recurrence relation for the number of representations of a positive integer as a sum of squares, Advances in Maths: Scientific Journal 11, No. 11 (2022) 1055-1060.
M. A. Pathan, H. Kumar, M. Muniru Iddrisu, J. López-Bonilla, Polynomial expressions for certain arithmetic functions, J. Mountain Res. 18, No. 1 (2023) 1-10.
D. Cvijovic, New identities for the partial Bell polynomials, Appl. Math. Lett. 24 (2011) 1544-1547.
M. Shattuck, Some combinatorial formulas for the partial r-Bell polynomials, Notes on Number Theory and Discrete Maths. 23, No. 1 (2017) 63-76.
M. A. Pathan, H. Kumar, J. D. Bulnes, J. López-Bonilla, Connection between partial Bell polynomials and 〖(q;q)〗_k; partition function, and certain q-hypergeometric series, J. Ramanujan Soc. Maths. Math. Sci. 10, No. 1 (2022) 1-12.
R. Sivaraman, J. D. Bulnes, J. López-Bonilla, Complete Bell polynomials and recurrence relations for arithmetic functions, European J. of Theoretical and Appl. Sci. 1, No. 3 (2023) 167-170.
Venkatasubbu, P., & Ganesh, M. (2019). Used Cars Price Prediction using Supervised Learning Techniques. In International Journal of Engineering and Advanced Technology (Vol. 9, Issue 1s3, pp. 216–223). https://doi.org/10.35940/ijeat.a1042.1291s319
Purchase Decision towards Textile and Apparel Products. (2019). In International Journal of Recent Technology and Engineering (Vol. 8, Issue 2S11, pp. 3239–3247). https://doi.org/10.35940/ijrte.b1423.0982s1119
Singh, R., & sharma, Dr. T. (2020). A Disquisition of Significant Role of Feedback and Counseling on Workforce Performance - Reference of I.T. Companies (delhi-ncr region). In International Journal of Management and Humanities (Vol. 4, Issue 11, pp. 46–52). https://doi.org/10.35940/ijmh.k1063.0741120
Subaraj. M, A., Raj. J, B., Prince. R, M. R., Devadhas.G, *Glan, & Singh. S, C. E. (2019). Corrosion rate of Al-Si Alloy Reinforced with B4C Nanoparticle prepared by Powder Metallurgy Method using RSM. In International Journal of Innovative Technology and Exploring Engineering (Vol. 9, Issue 1, pp. 4677–4682). https://doi.org/10.35940/ijitee.a4650.119119
Puranik, A. G. (2023). On the Results of Coffy and Moli. In Indian Journal of Advanced Mathematics (Vol. 3, Issue 1, pp. 8–11). https://doi.org/10.54105/ijam.a1142.043123