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

3. Positivity of Constants Related to Elliptic Curves, PDF , Link , Journal of Number Theory, Dec. 2015

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, Pages 353–368

6. On the Order of a Modulo n, on Average, PDF , Link , International Journal of Number Theory, Dec. 2016

7. The Average Number of Divisors of the Euler Function, PDF , accepted for publication in Ramanujan Journal