Research

I am interested in additive combinatorics, discrete Fourier analysis, geometric measure theory, and discrete geometry.

Publications

1. F. Rakhmonov, Distribution of similar configurations in subsets of F_q^d, Discrete Mathematics, (2023). [arXiv] [doi] 

2. A. Iosevich, D. Koh, and F. Rakhmonov, The quotient set of the quadratic distance set over finite fields, Forum Mathematicum, (2024). [arXiv] [doi]

3. P. Bhowmik and F. Rakhmonov, Near optimal thresholds for existence of dilated configurations in F_q^d, Bulletin of the Australian Mathematical Society, (2024). [arXiv] [doi]

4. P. Bhowmik, A. Greenleaf, A. Iosevich, S. Mkrtchyan, and F. Rakhmonov, Similar point configurations via group actions, Illinois Journal of Mathematics, (2025). [arXiv] [doi]

Preprints

1. J. M. Fraser and F. Rakhmonov, Exceptional projections in finite fields: Fourier analytic bounds and incidence geometry, accepted for publication in Mathematische Zeitschrift, (2025). [arXiv] 

2. J. M. Fraser and F. Rakhmonov, An improved L² restriction theorem in finite fields, accepted for publication in Proceedings of the American Mathematical Society, (2025). [arXiv]

3. H. Kang, D. Koh, and F. Rakhmonov, The Erdős-Falconer distance problem between arbitrary sets and k-coordinatable sets in finite fields, (2025). [arXiv] 

4. J. M. Fraser and F. Rakhmonov, Lp  averages of the discrete Fourier transform and applications, accepted for publication in Springer Proceedings in Mathematics & Statistics, "Combinatorial and Additive Number Theory VII", (2025). [arXiv]

My coauthors: 

Allan Greenleaf (1)

Alex Iosevich (2)

Pablo Bhowmik (2)

Jonathan Fraser (3)

Doowon Koh (2)

Sevak Mkrtchyan (1)

Hunseok Kang (1)