Research & Publications 

Published Papers

1. R. Barman, A. Jakhar, R. Kalwaniya, and P. Yadav, Monogeneity and arithmetic of number fields generated by certain polynomial families, J. Pure Appl. Algebra 230 (2026), no. 9, Paper No. 108328. MR5091733.

2. A. Jakhar, R. Kalwaniya, and P. Yadav, A study of monogeneity of trinomial compositions: qualitative and quantitative aspects, J. Pure Appl. Algebra 230 (2026), no. 4, Paper No. 108231, 24 pp. MR5046175.

3. A. Jakhar, R. Kalwaniya, and K. Srinivas, On monogenity of number fields and Galois group, Int. J. Number Theory 21 (2025), no. 8, 1995–2013. MR4925475.

4. A. Jakhar, R. Kalwaniya, and P. Yadav, A study of monogenity of binomial composition, Acta Arith. 221 (2025), no. 4, 387–395. MR5078391.

5. A. Jakhar and R. Kalwaniya, On the second irreducibility theorem of I. Schur, Acta Math. Hungar. 174 (2024), no. 2, 289–298. MR4852064.

6. A. Jakhar, R. Kalwaniya, and P. Yadav, On the monogenity and Galois group of certain classes of polynomials, Math. Slovaca 74 (2024), no. 5, 1147–1154. MR4808742.

Preprints

7. A. Jakhar, R. Kalwaniya, S. Laishram, and P. Yadav, On the index of polynomial compositions over valued fields, submitted, 2026. arXiv:2610.02111
   Summary: We study the monogeneity of compositions f(h(xᵗ)), where f is monic and h is a trinomial. We give an explicit discriminant formula and, over arbitrary Krull valuation rings, a complete criterion for monogeneity in terms of f and square-free conditions on f(b) and the critical values of h. The results extend to polynomial iterates, giving new infinite towers of monogenic fields. Assuming the abc-conjecture, f and f∘h_b are simultaneously monogenic for a positive proportion of b.

8. A. Jakhar, R. Kalwaniya, A. Ray, and B. Roy, On the distribution of shapes of sextic pure number fields, submitted, 2026. arXiv:2601.09411
   Summary: Explicit shapes of pure sextic fields ℚ(⁶√m) in all 20 local Types, and equidistribution of these shapes (ordered by discriminant) along torus orbits, with a limiting measure that is the product of a continuous and a discrete measure.

9. A. Jakhar, R. Kalwaniya, and M. Ram, Determination of class numbers of imaginary bicyclic biquadratic fields, submitted, 2025. arXiv:2509.13153
   Summary: A method to list all imaginary bicyclic biquadratic fields of class number n, with their class groups, from imaginary quadratic fields of class number dividing 2n. It gives complete lists for n = 4, 6, 7 (408, 552 and 277 fields).