I am interested in exploring topics related to prime numbers. In particular, my research interests so far lies in the intersection of Analytic Number Theory, Additive Combinatorics, Harmonic Analysis, and Ergodic Theory. Here is my long research statement, short research statement, and shorter research statement.
Here are my papers. For more information, please contact me or check my google scholar page. Manuscripts for the expected items can be sent upon request.
Mousavi, H. Variational Estimates for Möbius-Weighted Polynomial Multiple Ergodic Averages. In Prepration, Expected in Spring 2026.
Mousavi, H. On Equidistribution of Prime Squares and Its Applications. In Prepration, Expected in 2025.
Giannitsi, C. Miheisi, N. Mousavi, H. Averages With the Gaussian Divisor: Weighted Inequalities and the Pointwise Ergodic Theorem. Arxiv Link.
Giannitsi, C. Miheisi, N. Mousavi, H. On Ergodic Averages weighted by Divisors at the Endpoints. In Prepration, Expected in 2025.
Krause, B. Mousavi, H. Tao, T. Teravainen , J. Quantitative Bounds For Sets Lacking Polynomial Progressions With Shifted Prime Difference. In Prepration, Expected in 2025.
Fragkos, A. Fornal, J. Kreause, B. Lacey, M. Mousavi, H. Sun, YC. The Wiener Wintner and Return Times Theorem Along the Primes. In Prepration, Expected in 2025.
Iosevich, A. Krause, B. Mousavi, H. An Approach To Endpoint Problems in Oscillatory Singular Integrals. Math. Z. 2025. Arxiv Link.
Lacey, M. Mousavi, H. Rahimi, Y. Vempati, M. A Density Theorem for Higher Order Sums of Prime Numbers. Submitted. 2025. Arxiv Link.
Krause, B. Mousavi, H. Tao, T. Teravainen, J. Pointwise Convergence of Bilinear Polynomial Averages Over the Primes. Ergodic Theory and Dynamical Systems. 2025. Arxiv Link.
Giannitsi, C. Miheisi, N. Mousavi, H. Pointwise Ergodic Theorem along Gaussian Integers with weighted sums. Submitted. 2025. Arxiv Link.
Croot, E. Mousavi, H. Schmidt, M. On a Conjecture of Graham on the p-Divisibility of Central Binomial Coefficients. Mathematika. 2024. here.
Croot, E. Mousavi, H. On a Class of Sums with Unexpectedly High Cancellation, and its Applications. 2024. Arxiv Link.
Giannitsi, C. Krause, B. Lacey, M. Mousavi, H. Rahimi, Y. Averages Over the Gaussian Primes: Goldbach's Conjecture and Improving Estimates, Submitted. 2023. Arxiv Link.
Shahhosseini, E. Dastbasteh, R. Dinh, HQ. Mousavi, H. On the Structure of Ideals in a Family of Skew Polynomial Rings, Journal of Algebra and its applications. 2023. here.
Giannitsi, C. Lacey, M). Mousavi, H. Rahimi, Y. Improving and Maximal Inequalities for Primes in Progressions. Banach Journal of Mathematical Analysis. 2022. Arxiv Link.
Mousavi, H. Padashnik, F. Qureshi, A. On Reduced Archimedean Skew Power Series Rings. Journal of Algebra and Its Applications. 2022. Arxiv Link.
Lacey, M. Mousavi, H. Rahimi, Y. Endpoint Lp-lmproving Estimates for Prime Averages. Math Research Letters. 2021. Arxiv Link.
Mousavi, H. Schmidt , M. Factorization Theorems for Relatively Prime Divisor Sums, GCD Sums and Generalized Ramanujan Sums. Published in The Ramanujan Journal. 2021. here.
Mousavi, H. Padashnik, F. Qureshi, A. On Reduced Archimedean Skew Power Series Rings. Journal of Algebra and its Applications 2020. here.
Mousavi, H. Mohammadi, R. Rahimi, S. On Skew Cyclic Codes over a Finite Ring. Published in Iranian Journal of Mathematical Sciences and Informatics. 2019. here.
Dastbasteh, R. Mousavi, H. Abualrub, T. Haghighat, J. Aydin, N. Characterization of the Skew Cyclic Codes over Fp+uFp. International Journal of Information and Coding Theory 2018. here.
Mousavi, H. Moussavi, A. Rahimi, S. Skew Cyclic Codes over Fp+vFp+v^2Fp. Bulletin of Korean Mathematics. 2018. here.
Mousavi, H. Ahmadi, B. Rahimi, S. A New Approach to Decrease the Computational Complexity of E-voting Protocols. Transactions on Emerging Telecommunications Technologies. 2017. here.
Mousavi, H. Haghighat, J. Hamuda, W. DastBaste, R. Analysis of a Subset Selection Scheme for Wireless Sensor Networks in Time-Varying Fading Channels. IEEE Transaction on Signal Processing. 2016. here.
Mousavi ,H. Haghighat, J. Hamuda, W. A Relay Subset Selection Scheme for Wireless Sensor Networks Based on Channel State Information. IEEE International Conference on Communications (ICC). 2016. Malysia. here
Here is my PhD Thesis at Georgia Tech. Application of Circle Method in Five Number Theory Problems.
My Master's thesis at Sabanci can be found here. The Hardy-Ramanujan-Rademacher Expansion for the Partition Function and its Extensions.