A diffeomorphic approach to interpolating prime series and solving diophantine equations

  • Post author:
  • Ramaraju Yadav E Orchid logo
  • Chandra Bhan Singh Orchid logo

Journal Name: Discover Engineering: An International Journal

DOI: https://doi.org/10.51470/DE.2025.6.1.27

Keywords: Diophantine Equations; Diffeomorphic Approach; prime series

Abstract

A diffeomorphic pair (p(x),p^(-1) (x)) is constructed in this work by interpolating the prime series with a suitable quadric spline. The prime counting function and the prime series are smooth analogues of these continuously differentiable functions, which capture the key behaviour of prime numbers. Estimates for Diophantine equations over primes are obtained by using the function p^(-1) (x) The research also investigates the possibility of using this function to the analysis of the prime number theorem’s error term in the von Koch estimate; this theorem is closely related to the Riemann Hypothesis.

Download this article as

Reference

  1. Milgram, M. (2020). Research Article An Integral Equation for Riemann’s Zeta Function and Its Approximate Solution.
  2. Min, H., Tarmoun, S., Vidal, R., & Mallada, E. (2021, July). On the explicit role of initialization on the convergence and implicit bias of overparametrized linear networks. In International Conference on Machine Learning (pp. 7760-7768). PMLR.
  3. Xu, L., Chatterton, S., & Pennacchi, P. (2021). Rolling element bearing diagnosis based on singular value decomposition and composite squared envelope spectrum. Mechanical Systems and Signal Processing, 148, 107174.
  4. Werner, F. (2015). On convergence rates for iteratively regularized Newton-type methods under a Lipschitz-type nonlinearity condition. Journal of Inverse and Ill-Posed Problems, 23(1), 75-84.
  5. Mavrodiev, S. C., & Deliyergiyev, M. A. (2017). Computation of the Binding Energies in the Inverse Problem Framework. In EXOTIC NUCLEI: EXON-2016 Proceedings of International Symposium (pp. 330-337).
Post Views: 45