Fedor Pakovich
Email: pakovich at math dot bgu dot ac dot il
Professor
Department of Mathematics
Ben Gurion University of the Negev
P.O.B. 653 Beer Sheva
8410501 ISRAEL
Office: Deichman 310
Research interests: Complex analysis, Number Theory, Complex and Arithmetic Dynamics
Preprints
Level curves of rational functions and unimodular points on rational curves, (with I. Shparlinski), pdf
Algebraic curves Aol(x)-U(y)=0 and
arithmetic of orbits of rational functions. pdf
On generalized Lattès maps. pdf
Finiteness theorems for commuting
and semiconjugate rational functions. pdf
Publications
Semiconjugate rational functions: a dynamical approach, Arnold Math. J., (2018), online first, pdf
On rational functions whose
normalization has genus zero or one,
Acta. Arith., 182 (2018) , 73-100. pdf
On algebraic curves A(x)-B(y)=0 of genus zero,
Math. Z., Vol. 288, Issue 1, (2018), 299-310. pdf
Davenport-Zannier Polynomials over Q, (with. A. Zvonkine),
Int. J. Number Theory, 14 (2018), no. 4, 925-974. pdf
Polynomial semiconjugacies,
decompositions of iterations, and invariant curves,
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Vol. XVII (2017), 1417-1446. pdf
Recomposing rational functions,
Int. Math. Res. Not., (2017), online first. pdf
Solution of the parametric Center
Problem for Abel Equation,
J. Eur. Math. Soc., 19 (2017), no. 8, 2343-2369. pdf
On decompositions of trigonometric
polynomials,
Israel J. Math., 217 (2017), 337-353. pdf
On semiconjugate
rational functions,
Geom. Funct. Anal., 26 (2016), 1217-1243. pdf
Algebraic Geometry of the
Center-Focus problem for Abel Differential Equation,
(with Y. Yomdin, M. Briskin),
Ergodic Theory and Dynam. Sys.,Volume 36, Issue 3, (2016) 714–744. pdf
Parametric Center-Focus Problem for
Abel Equation, (with Y. Yomdin, M. Briskin),
Qual. Theory Dyn. Syst., ,
(2014) 13:289-303. pdf
Weak and strong composition
conditions for the Abel differential equation,
Bull. Sci. Math., 138 (2014), 993-998. pdf
Minimum Degree of the Difference of
Two Polynomials over Q and Weighted Plane Trees,
(with. A. Zvonkine),
Selecta Math., 20, no. 4 (2014), 1003-1065. pdf
Moments on Riemann surfaces and hyperelliptic Abelian integrals,
(with L. Gavrilov),
Comm. Math. Helvetici, 89, No 1, (2014) pp. 125–155. pdf
On rational functions orthogonal to
all powers of a given rational function on a curve,
Moscow Math. Journal, Volume 13, Issue 4, (2013) 693–731.
pdf
Generalized "second Ritt theorem" and explicit solution of the polynomial
moment problem,
Compositio Math. 149 (2013), 705-728. pdf
Algebraic curves P(x)-Q(y)=0 and functional equations,
Complex Var. and Elliptic Equ., 56 (2011), no. 1-4,
199–213. pdf
Moment Vanishing Problem and
Positivity: Some Examples
(with J. P. Francoise, Y. Yomdin, W. Zhao),
Bull. Sci. Math., 135 (2011), no. 1, 10-32. pdf
Jordan-Holder theorem for imprimitivity systems and maximal decompositions of
rational functions (with M. Muzychuk),
Proc. Lond. Math. Soc., 102 (2011)
, no. 1, 1-24. pdf
Laurent polynomial moment problem:
a case study
(with A. Zvonkin and C. Pech),
Contemp. Math., 532 (2010), 177-194. pdf
On the equation P(f)=Q(g),
where P,Q are polynomials and f,g are entire
functions,
Amer. Journal of Math., 132 (2010), no. 6, 1591-1607. pdf
Prime and composite Laurent
polynomials,
Bull. Sci. Math., 133 (2009), 693-732. pdf
Solution of the polynomial moment
problem
(with M. Muzychuk).
Proc. Lond. Math. Soc., 99 no. 3, 633–657 (2009). pdf
Solution of the Hurwitz problem for
Laurent polynomials,
J. Knot Theory Ramifications, 18, No. 2, 271-302 (2009). pdf
On trees covering chains or stars,
J. Math. Sci., New York, 158, No. 1, 148-154 (2009). pdf
Arithmetics of conservative polynomials and yet another
action of the group Gal(Q/Q) on plane trees,
J. Théor. Nombres Bordeaux,
20, 205-218 (2008). pdf
On analogues of the theorems for
rational functions with at most two poles,
Russ. Math. Surv. 63, No. 2, 386-387 (2008). pdf
On polynomials sharing preimages of
compact sets, and related questions,
Geom. Funct. Anal, 18,
No. 1, 163-183 (2008). pdf
On the functional equation F(A(z))=G(B(z)), where A,B are polynomial and F,G are
continuous functions,
Math. Proc. Cam. Phil. Soc., 143, No. 2, 469-472
(2007), pdf
Remark on the Chebotarev
theorem about roots of unity,
Integers 7 (2007), A18 (electronic). pdf
On polynomials orthogonal to all
powers of a given polynomial on a segment,
Bull. Sci. Math. 129 (2005), 749-774. pdf
Cauchy type integrals of Algebraic functions
(with N. Roytvarf and Y. Yomdin),
Israel J. Math., Vol. 144 (2004), 221-291. pdf
On polynomials orthogonal to all
powers of a Chebyshev polynomial on a segment,
Israel J. Math., Vol. 142 (2004), 273—283. pdf
Polynomial moment problem,
Addendum to the paper by Y. Yomdin,
Mosc. Math. J., 3(2003), no. 3, 1167-1195. pdf
On the polynomial moment problem,
Math. Res. Lett., 10, no. 2-3, 401--410 (2003). pdf
A counterexample to the
``composition conjecture'',
Proc. Amer. Math. Soc. 130, 3747-3749 (2002). pdf
On trees admitting morphisms onto
hedgehogs or onto chains,
Russ. Math. Surv. 55, No.3,
593-594 (2000).
Combinatoire des arbres planaires et arithmetique
des courbes hyperelliptiques,
Ann. Inst. Fourier 48, No.2, 323-351 (1998). pdf
A remark on complex polynomials of
least deviation
(with I. V. Ostrovskii and M. G. Zaidenberg),
Int. Math. Res. Not. 1996, No.14, 699-703 (1996). pdf
Sur un probleme d'unicite pour les functions meromorphes,
C. R. Acad. Sci., Paris (Ser. I) 323, No.7, 745-748 (1996). ps
Elliptics polynomials,
Russ. Math. Surv. 50, No.6, 1292-1294 (1995).
Locally nilpotent derivations of polynomial
rings,
Math. Notes 58, No.2, 890-891 (1995)