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.

Research Interests

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, American Journal of Mathematics 143 (2021), no. 6, pp. 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. 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.
    arXiv


17. Uniform estimates for friable polynomials over finite fields
    O. Gorodetsky, to appear in Discrete Analysis.
    Accepted version arXiv

Preprints

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


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


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


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


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


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


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


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

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PhD Thesis

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

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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).

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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 F_q[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.

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Contact Details

Office: N2.05
E-mail:

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Last updated: July 28, 2023.