Publications and accepted manuscripts

1. A polynomial analogue of Landau's theorem and related problems
   O. Gorodetsky, Mathematika 63 (2017), no. 2, 622-665.
   Journal arXiv


2. On certain degenerate Whittaker Models for cuspidal representations of GL_k.n(F_q)
   O. Gorodetsky, Z. Hazan, Math. Z. 291 (2019), no. 1-2, 609-633.
   Journal arXiv


3. Roots of Polynomials and the Derangement Problem
   L. Bary-Soroker, O. Gorodetsky, Amer. Math. Monthly 125 (2018), no. 10, 934-938.
   Journal arXiv


4. q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
   O. Gorodetsky, Int. J. Number Theory 15 (2019), no. 9, 1919-1968.
   Journal arXiv


5. Irreducible polynomials over F_2^r with three prescribed coefficients
   O. Gorodetsky, Finite Fields Appl. 56 (2019), 150-187.
   Journal arXiv


6. Mean values of arithmetic functions in short intervals and in arithmetic progressions in the large-degree limit
   O. Gorodetsky, Mathematika 66 (2020), no. 2, 373–394.
   Journal arXiv


7. The variance of the number of sums of two squares in F_q[T] in short intervals
   O. Gorodetsky, B. Rodgers, Amer. J. Math. 143 (2021), no. 6, 1703-1745.
   Journal arXiv


8. Chebotarev density theorem in short intervals for extensions of F_q(T)
   L. Bary-Soroker, O. Gorodetsky, T. Karidi, W. Sawin, Trans. Amer. Math. Soc. 373 (2020), 597-628.
   Journal arXiv


9. Correlation of arithmetic functions over F_q[T]
   O. Gorodetsky, W. Sawin, Math. Ann. 376 (2020), no. 3-4, 1059-1106.
   Journal arXiv


10. Multiplicative arithmetic functions and the generalized Ewens measure
    D. Elboim, O. Gorodetsky, Israel J. Math. 262 (2024), no. 1, 143–189.
    Journal arXiv


11. Traces of powers of matrices over finite fields
    O. Gorodetsky, B. Rodgers, Trans. Amer. Math. Soc. 374 (2021), 4579-4638.
    Journal arXiv


12. On the variance of squarefree integers in short intervals and arithmetic progressions
    O. Gorodetsky, K. Matomäki, M. Radziwiłł, B. Rodgers, Geom. Funct. Anal. 31 (2021), no. 1, 111-149.
    Journal arXiv


13. Uniform estimates for almost primes over finite fields
    D. Elboim, O. Gorodetsky, Proc. Amer. Math. Soc. 150 (2022), 2807-2822.
    Journal arXiv


14. New representations for all sporadic Apéry-like sequences, with applications to congruences
    O. Gorodetsky, Exp. Math. 32 (2023), no. 4, 641-656.
    Journal arXiv


15. Sums of two squares are strongly biased towards quadratic residues
    O. Gorodetsky, Algebra & Number Theory 17 (2023), no. 3, 775-804.
    Journal arXiv


16. Squarefrees are Gaussian in short intervals
    O. Gorodetsky, A. P. Mangerel, B. Rodgers, J. Reine Angew. Math. (Crelle's journal) 795 (2023), 1-44.
    Journal arXiv


17. Uniform estimates for smooth polynomials over finite fields
    O. Gorodetsky, Discrete Anal. (2023), Paper No. 16, 31 pp.
    Journal arXiv


18. Smooth integers and the Dickman ρ function
    O. Gorodetsky, J. Anal. Math. 151 (2023), no. 1, 139-169.
    Journal arXiv


19. Smooth integers and de Bruijn's approximation Λ
    O. Gorodetsky, appeared online in Proc. Roy. Soc. Edinburgh Sect. A.
    Journal arXiv


20. Magic squares, the symmetric group and Möbius randomness
    O. Gorodetsky, Monatsh. Math. 204 (2024), no. 1, 27-46.
    Journal arXiv


21. Equidistribution of high traces of random matrices over finite fields and cancellation in character sums of high conductor
    O. Gorodetsky, V. Kovaleva, Bull. Lond. Math. Soc. 56 (2024), no. 7, 2315-2337.
    Journal arXiv


22. On an Erdős–Kac-type conjecture of Elliott
    O. Gorodetsky, L. Grimmelt, Q. J. Math. 75 (2024), no. 2, 695-713.
    Journal arXiv


23. The variance of integers without small prime factors in short intervals
    O. Gorodetsky, Math. Z. 308 (2024), no. 4, Paper No. 59.
    Journal arXiv


24. On Erdős sums of almost primes
    O. Gorodetsky, J. D. Lichtman, M. D. Wong, to appear in Comptes Rendus Mathematique.
    arXiv


25. Smooth permutations and polynomials revisited
    O. Gorodetsky, to appear in Mathematical Proceedings of the Cambridge Philosophical Society.
    arXiv

Preprints

1. A short proof of Helson's conjecture
   O. Gorodetsky, M. D. Wong, submitted.
   arXiv


2. Martingale central limit theorem for random multiplicative functions
   O. Gorodetsky, M. D. Wong, submitted.
   arXiv


3. Sharp local estimates for smooth numbers
   O. Gorodetsky, submitted (available upon request).
   

PhD Thesis

The variance of sums of arithmetic functions
Tel Aviv University Theses (Local copy)

Comments

1. Paper no. 2 supersedes arXiv preprint 1611.06502. In Theorem 1 of paper no. 2 as stated, we should assume ϴ restricted to F_n^* is regular (in addition to ϴ being regular). The theorem is true for all other regular ϴ if it is interpreted as equality of virtual characters.
2. Here you can find combinatorial questions related to paper no. 4.
3. Here you can find the SageMath code that generates the graphs presented in the paper no. 7. The function generate_all_graphs() generates the various graphs, but one first must run the MATLAB files 1 and 2 in the same folder.
4. In subsection 3.4 of paper no. 14, it is mentioned that empirically, two symmetric Laurent polynomials given explicitly in that subsection, have certain constant term series (coinciding with the generating functions of sequences known as s₁₈ and (γ)). This empirical observation has since been verified rigorously using the HolonomicFunctions Mathematica package.
5. Here you can find unpolished notes from a talk, based mostly on paper no. 18 (on smooth integers and the Dickman function).
6. At this link you will find slides and recording of a talk, based mostly on papers no. 17 and no. 19 (on smooth integers and polynomials via the indirect saddle point method).