Publications of Lior Bary-Soroker

Papers in Journals

Note that arXiv version may be slightly different from journal version.
  1. L. Bary-Soroker, Diamond theorem for a finitely generated free profinite group, Math. Ann., 336 (4), 949-961 (2006).
    arXiv, journal
  2. L. Bary-Soroker and M. Jarden, PAC fields over finitely generated fields, Math. Z., 260 (2), 329-334 (2008).
    arXiv, journal
  3. L. Bary-Soroker, On the characterization of Hilbertian fields, Int. Math. Res. Not., 2008 Art. ID rnn 089, 10 pp. (2008).
    arXiv, journal
  4. L. Bary-Soroker, Dirichlet's theorem for polynomial rings, Proc. Amer. Math. Soc., 137, 73-83 (2009).
    arXiv, journal
  5. L. Bary-Soroker, On pseudo algebraically closed extensions of fields, J. Algebra, 322 (6), 2082-2105 (2009).
    arXiv, jouranl
  6. L. Bary-Soroker and D. Kelmer, On PAC extensions and scaled Trace forms, Israel J. Math., 175, (1), 113-124 (2010).
    arXiv, journal
  7. L. Bary-Soroker, D. Haran, and D. Harbater, Permanence criteria for semi-free profinite groups, Math. Ann., 348 (3), 539-563 (2010).
    arXiv, journal
  8. L. Bary-Soroker, Projective pairs of profinite groups, J. of Algebra, 324 (9), 2112-2128 (2010).
    arXiv, journal
  9. L. Bary-Soroker and N. D. Tan, On p-embedding problems in characteristic p, J. Pure Appl. Algebra, 215 (10), 2533-2537 (2011).
    arXiv, journal
  10. L. Bary-Soroker, K. Stevenson, and P. Zalesskii, Subgroups of profinite surface groups, Math. Res. Lett., 18 (3), 459-471 (2011).
    arXiv, journal
  11. L. Bary-Soroker, Irreducible values of polynomials, Adv. Math., 229 (2), 854-874 (2012).
    arXiv, journal
  12. L. Bary-Soroker, Irreducibility and embedding problems, J. Algebra, 357 26-33 (2012).
    arXiv, journal
  13. L. Bary-Soroker, Hardy-Littlewood tuple conjecture over large finite fields, Int. Math. Res. Not., 2012, Art. ID rns 249, 8 pp. (2012).
    arXiv, journal
  14. L. Bary-Soroker and M. Kumar, Subgroup structure of fundamental groups in positive characteristic, Comm. Algebra, 41 (9), (2013).
    arXiv, journal
  15. L. Bary-Soroker and E. Paran, Fully Hilbertian fields, Israel J. Math., 194 (2), 507-538 (2013).
    arXiv, journal
  16. L. Bary-Soroker and M. Jarden, On the Bateman-Horn conjecture about polynomial rings, Munster J. Math, 5, 41-58 (2012).
    arXiv, journal
  17. L. Bary-Soroker and A. Fehm, Random Galois extensions of Hilbertian fields, J. The'or. Nombres Bordeaux, 24 (1), 31-42 (2013).
    arXiv, journal
  18. L. Bary-Soroker, A. Fehm, and G. Wiese, Hilbertian fields and Galois representations, J. Reine Angew. Math., DOI 10.1515/crelle-2013-0116.
    arXiv, journal
  19. L. Bary-Soroker, A. Fehm, and S. Petersen, On varieties of Hilbert type, Ann. Inst. Fourier (Grenoble) 64 (2014), no. 5, 1893-1901.
    arXiv, journal
  20. E. Bank, L. Bary-Soroker, and L. Rosenzweig, Prime polynomials in short intervals over large finite fields, Duke Math. J. 164 (2015), no. 2, 277-295.
    arXiv, jornal
  21. J. C. Andrade, L. Bary-Soroker, and Z. Rudnick, Shifted convolution and the Titchmarsh divisor problem over F_q[t], Philos. Trans. A 373 (2015), no. 2040, 20140308, 18 pp.
    arXiv, journal
  22. E. Bank and L. Bary-Soroker, Prime polynomial values of linear functions in short intervals, J. Number Theory 151 (2015), 263-275.
    arXiv, journal
  23. L. Bary-Soroker, M. Jarden, and D. Neftin, The Sylow subgroups of the absolute Galois group Gal(Q), Adv. Math. 284 (2015), 186-212.
    arXiv, journal
  24. L. Bary-Soroker, Y. Smilansky, A. Wolf, On the Function Field Analogue of Landau's Theorem on Sums of Squares, Finite Fields Appl. 39 (2016) 195-215.
    arXiv, journal
  25. L. Bary-Soroker and Gady Kozma, Is a bivariate polynomial with plus minus 1 coefficients irreducible? Very likely!,
    arXiv:1602.06530, Int. J. Number Theory, in press
  26. L. Bary-Soroker, Prime Polynomials in Function Fields, Snapshots of modern mathematics, MFO, No. 10/2016.
  27. E. Bank, L. Bary-Soroker, and A. Fehm, Sums of two squares in short intervals in polynomial rings over finite fields,
    arXiv:1509.02013, Am. J. Math., in press
  28. L. Bary-Soroker and A. Fehm, Correlations of sums of two squares and other arithmetic functions in function fields, International Mathematics Research Notices, , rnx250,
    arXiv:1701.04092, journal
  29. L. Bary-Soroker, M. Shusterman, and U. Zannier, Totally real subextensions, an appendix to Rel leaves of the Arnoux-Yoccoz surfaces by W. P. Hooper and B. Weiss,
    arXiv:1508.05363, Selecta Mathematica, in press


  1. L. Bary-Soroker and F. Legrand, On the number of ramified primes is specializations of function fields over Q,
  2. L. Bary-Soroker and Tomer M. Schlank, Sieves and the Minimal Ramification Problem,
  3. L. Bary-Soroker and Gady Kozma, Irreducible polynomials of bounded height,
  4. L. Bary-Soroker and Patrick Meisner, On the distribution of the rational points on cyclic covers in the absence of roots of unity,
  5. L. Bary-Soroker and Jakob Stix, Cubic twin prime polynomials are counted by modular form,


  1. S. Arias-de-Reyna, L. Bary-Soroker, and G. Wiese (Eds), Winter School on Galois Theory Volume 1: Luxembourg 2012, Travaux mathe'matiques 22, 238 pp.
  2. S. Arias-de-Reyna, L. Bary-Soroker, and G. Wiese (Eds), Winter School on Galois Theory Volume 2: Luxembourg 2012, Travaux mathe'matiques 23, 222 pp.

Papers in refereed proceedings

  1. L. Bary-Soroker and E. Paran, On totally ramified extensions of discrete valued fields,Arithmetic and geometry around Galois theory, 371-376, Progr. Math., 304, Birkhauser/Springer, Basel, 2013.
  2. L. Bary-Soroker and A. Fehm, Open problems in the theory of ample fields, Geometric and differential Galois theories, 1-11, Semin. Congr., 27, Soc. Math. France, Paris, 2013.
  3. L. Bary-Soroker and A. Fehm, On fields of totally S-adic numbers, Valuation theory in interaction, 11-15, EMS Ser. Congr. Rep., Eur. Math. Soc., Zurich, 2014.

papers in refereed educational journals

  1. L. Bary-Soroker and E. Leher, On the remainder in the Taylor theorem , The College Mathematics Journal, Volume 40, Number 5, November 2009, pp. 373-374(2).


  1. L. Bary-Soroker, Hilbertianity under algebraic extensions and Haar measure, M.Sc. Thesis, Hebrew or English.
  2. L. Bary-Soroker, Pseudo algebraically closed extensions, Ph. D. Thesis Hebrew or English.
  3. Letter to Bjorn Poonen, September 16, 2013

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