Ofir Gorodetsky

Since October 2020, I am a Postdoctoral Research Associate in Analytic Number Theory at the University of Oxford, employed by Prof. James Maynard's 'PRIMES' ERC grant.
Starting August 2024, I will be an assistant professor at the Technion - Israel Institute of Technology.
Please feel welcome to ask me about math.

New: Slides, notes and videos section added.

Research Interests

Probabilistic number theory
Random matrix theory
Chebyshev's bias
Smooth and rough numbers
Finite fields and their applications

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 GLk.n(Fq)
    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 F2r 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 Fq[T] in short intervals
    O. Gorodetsky, B. Rodgers, American Journal of Mathematics 143 (2021), no. 6, pp. 1703-1745.
    Journal arXiv

  8. Chebotarev density theorem in short intervals for extensions of Fq(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 Fq[T]
    O. Gorodetsky, W. Sawin, Math. Ann. 376 (2020), no. 3-4, 1059-1106.
    Journal arXiv

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

  11. 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

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

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

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

  15. New representations for all sporadic Apéry-like sequences, with applications to congruences
    O. Gorodetsky, to appear in Experimental Mathematics.
    Journal arXiv

  16. Multiplicative arithmetic functions and the generalized Ewens measure
    D. Elboim, O. Gorodetsky, to appear in Israel Journal of Mathematics.

  17. Uniform estimates for smooth polynomials over finite fields
    O. Gorodetsky, Discrete Analysis 2023:16, 31 pp.
    Journal arXiv


  1. Magic squares, the symmetric group and Möbius randomness
    O. Gorodetsky, submitted.

  2. The variance of integers without small prime factors in short intervals
    O. Gorodetsky, submitted.

  3. Friable integers and the Dickman ρ function
    O. Gorodetsky, submitted. (Revised version available upon request.)

  4. Friable permutations and polynomials revisited
    O. Gorodetsky, submitted.

  5. Friable integers and de Bruijn's approximation Λ
    O. Gorodetsky, submitted.

  6. On Erdős sums of almost primes
    O. Gorodetsky, J. D. Lichtman, M. D. Wong, submitted.

  7. Equidistribution of high traces of random matrices over finite fields and cancellation in character sums of high conductor
    O. Gorodetsky, V. Kovaleva, submitted.

  8. On a conjecture of Elliott concerning a probabilistic variant of Titchmarsh's divisor problem
    O. Gorodetsky, L. Grimmelt

PhD Thesis

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

Slides, notes and videos

Here you can find notes from a recent talk, based mostly on preprint 3 (on smooth numbers and the Dickman function).
At this link you will find slides and recording of a talk, based mostly on preprint 5 and paper 17 (on smooth integers and polynomials via the indirect saddle point method).


Here you can find the SageMath code that generates the graphs presented in the paper "The variance of the number of sums of two squares in Fq[T] in short intervals". The functions generate_all_graphs() generates the various graphs, but one first must run the MATLAB files 1 and 2 in the same folder.

Contact Details

Office: N2.05
profile for Ofir Gorodetsky at MathOverflow, Q&A for professional mathematicians

Last updated: July 28, 2023.