1. Average Behaviors of Invariant Factors in Mordell-Weil Groups of CM Elliptic Curves Modulo p, PDF , Link , Finite Fields and Their Applications, Nov. 2014, pp. 178-190
2. Average of the First Invariant Factor of the Reductions of Abelian Varieties of CM Type, PDF , Link , International Journal of Number Theory, Mar. 2016, pp. 445-463
3. Positivity of Constants Related to Elliptic Curves, PDF , Link , Journal of Number Theory, Dec. 2015, pp. 54-63
4. Average Reciprocals of the Order of a Mod n, PDF , Link , Journal of Number Theory (2016), pp. 62-75
5. Average Results on the Order of a Mod p, PDF , Link , Journal of Number Theory, December 2016, pp. 353 368
6. On the Order of a Modulo n, on Average, PDF , Link , International Journal of Number Theory, Dec. 2016, pp. 2073-2080
7. The Average Number of Divisors of the Euler Function, PDF , Link , Ramanujan Journal, May 2017, pp. 155-183
8. Some Theorems on Multiplicative Orders modulo p, PDF , Link , Journal of Number Theory, March 2020, pp. 180-207
9. Binomial Probability of Prime Number of Successes (with Nilotpal Kanti Sinha), PDF , Link , Integers 20(2020), A99.
10. On the Equations ϕ(n)=ϕ(n+k) and ϕ(p-1)=ϕ(q-1), PDF , Link , International Journal of Number Theory, Vol. 17, No. 06, pp. 1287-1305 (2021)
11. Two Remarks on the Largest Prime Factors of n and n+1, PDF , Link , Journal of Integer Sequences, Vol 23 (2020), Article 20.10.1
12. On the Distribution of Lcm of k-Tuples and Related Problems, PDF , Link , Functiones et Approximatio, Commentarii Mathematici, 68(1): 19-39 (March 2023)
13. On the Reciprocal Sum of lcm of k-tuples, PDF , Link , Research in Number Theory volume 8, Article number: 44 (2022)