Dr. Ramesh is interested in number theory, algorithms, and computing. Currently his research is in two directions, one around Gauss’s primitive root conjecture and second on designing scalable algorithms for shock capturing. He is also working on constructing a necessary and sufficient condition for 2 being a primitive root of Sophie Germain primes and a few generalisation of Sophie Germain primes. Further he is working on connecting the various partitions of primes with 2 as primitive root of 2p + 1. On estimating this, the idea is to generalize it to more general primes and work on connecting the primitive root and the number of orbits of the permutation (p!).
Ramesh V.P., Makeshwari M, (2023).
Is a Sophie Germain Prime a Primitive Root of Safe Prime? Mathematical Association of America: Mathematics Magazine
Ramesh V.P., Makeshwari M, Saswati Sinha (2023).
Connecting primitive roots and permutations, Indian National Science Academy: Indian Journal of Pure and Applied Mathematic, https://doi.org/10.1007/s13226-023-00384-4
Ramesh V. P., Gowtham R, Saswati Sinha (2023).
A note on the sum of cubic residues with even and odd index, Indian National Science Academy: - Indian Journal of Pure and Applied Mathematics, https://doi.org/10.1007/s13226-023-00370-w
Ramesh V.P., Makeshwari M, (2023).
A note on generalized Sophie Germain primes: In the direction of Legendre’s extended Sophie Germain primes, Resonance - Indian Academy of Sciences, 923-928,
Ramesh V.P., Makeshwari M, (2022).
A Primitive Root p of 2p+1 is a Sophie Germain Prime, The American Mathematical Monthly, 129(6), p. 538, 2022 https://doi.org/10.1080/00029890.2022.2059961
Ramesh V. P., Gowtham R, Saswati Sinha (2022).
A Note on Cubic Residues Modulo n, Indian National Science Academy: - Indian Journal of Pure and Applied Mathematics, 54, 6265, doi: https://doi.org/10.1007/s13226-022-00230-z (2022)
Ramesh V.P., Makeshwari M, (2022).
Least primitive root of any safe prime is prime, The American Mathematical Monthly, 129(10), 971 https://doi.org/10.1080/00029890.2022.2115816
Gajendra Babu, Prithvi M, Kapil K. Sharma & Ramesh V.P. (2022)
A Robust Numerical Algorithm on Harmonic Mesh for Parabolic Singularly Perturbed Convection-Diffusion Problems with Time Delay, Numerical Algorithms, Numerical Algorithms, 91, 615634
Ramesh V.P., Janakiraman S., Prithvi M. & Narayani G. (2022).
A new a priori estimation for singularly perturbed problems with discontinuous data, Indian Journal of Pure and Applied Mathematics, 53, pages813825 (
Ramesh V.P., Kapil K. Sharma, Priyanga B., Narayani G. (2021).
A uniformly convergent upwind scheme on harmonic mesh for singularly perturbed turning point problems, International Journal for Computational Methods in Engineering Science and Mechanics, 376-385
