Ofir Gorodetsky אופיר גורודצקי

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.

Research Interests

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

Publications and accepted manuscripts

All works are available on my arXiv page. Below they are sorted by chronological arXiv appearance. Journal versions typically match arXiv versions.
  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. Multiplicative arithmetic functions and the generalized Ewens measure
    D. Elboim, O. Gorodetsky, to appear in Israel Journal of Mathematics.
    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, No. 4, 641-656 (2023).
    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, 1-44 (2023).
    Journal arXiv

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

  18. Smooth integers and the Dickman ρ function
    O. Gorodetsky, Journal d'Analyse Mathématique 151, No. 1, 139-169 (2023).
    Journal arXiv

  19. Smooth integers and de Bruijn's approximation Λ
    O. Gorodetsky, appeared online in Proceedings of the Royal Society of Edinburgh Section A.
    Journal arXiv

  20. Magic squares, the symmetric group and Möbius randomness
    O. Gorodetsky, appeared online in Monatshefte für Mathematik.
    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, to appear in the Bulletin of the London Mathematical Society.
    arXiv


Preprints

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

  2. Friable permutations and polynomials revisited
    O. Gorodetsky, submitted.
    arXiv

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

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

PhD Thesis

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

Slides, notes and videos

Here you can find unpolished notes from a talk, based mostly on paper 18 (on smooth numbers and the Dickman function).
At this link you will find slides and recording of a talk, based mostly on papers 17 and 19 (on smooth integers and polynomials via the indirect saddle point method).

Code

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
E-mail:
profile for Ofir Gorodetsky at MathOverflow, Q&A for professional mathematicians

Last updated: April 4, 2024.