Publications of Michael Zieve

Michael E. Zieve

Email: zieve@umich.edu
Homepage: http://www.math.lsa.umich.edu/~zieve

Papers

44. Planar monomials in characteristic 2, with Z. Scherr, submitted, arXiv:1302.1244.

43. Planar functions and perfect nonlinear monomials over finite fields, submitted, arXiv:1301.5004.

42. Exceptional polynomials, pp. 229–233 in: Handbook of Finite Fields, CRC Press, 2013.

41. Value sets of polynomials, with G. Mullen, pp. 225–229 in: Handbook of Finite Fields, CRC Press, 2013.

40. The Mordell-Lang question for endomorphisms of semiabelian varieties, with D. Ghioca and T. Tucker, J. Théor. Nombres Bordeaux 23 (2011), 645–666.

39. Chebyshev mappings of finite fields, with J. Rosen, Z. Scherr and B. Weiss, Amer. Math. Monthly 119 (2012), 151–155.

38. Two questions on polynomial decomposition, with B. Wyman, Quarterly Journal of Math. (Oxford) 63 (2012), 507–511.

37. On hyperbolic fixed points in ultrametric dynamics, with K.-O. Lindahl, p-Adic Numbers, Ultrametric Analysis and Applications 2 (2010), 232–240.

36. An equality between two towers over cubic fields, Bull. Braz. Math. Soc., to appear, arXiv:0905.4921.

35. Classes of permutation polynomials based on cyclotomy and an additive analogue, pp. 355–359 in: Additive Number Theory, Springer, 2010, arXiv:0810.2830.

34. On a theorem of Carlitz, submitted, arXiv:0810.2834.

33. Linear relations between polynomial orbits, with D. Ghioca and T. Tucker, Duke Math. J. 161 (2012), 1379–1410. arXiv:0807.3576.

32. On Ritt's polynomial decomposition theorems, with P. Müller, submitted, arXiv:0807.3578.

31. Uniform bounds on pre-images under quadratic dynamical systems, with X. Faber, B. Hutz, P. Ingram, R. Jones, M. Manes and T. Tucker, Math. Research Letters 16 (2009), 87–101. arXiv:0805.0441.

30. Nonisomorphic curves that become isomorphic over extensions of coprime degrees, with D. Goldstein, R. Guralnick and E. Howe, J. Algebra 320 (2008), 2526–2558, arXiv:0801.4614.

29. Analogues of the Jordan-Hölder theorem for transitive G-sets, with G. Kuperberg and R. Lyons, submitted, arXiv:0712.4142.

28. Decompositions of Laurent polynomials, submitted, arXiv:0710.1902.

27. A new family of exceptional polynomials in characteristic two, with R. Guralnick and J. Rosenberg, Annals of Math. 172 (2010), 1367–1396, arXiv:0707.1837.

26. Polynomials with PSL(2) monodromy, with R. Guralnick, Annals of Math. 172 (2010), 1321–1365, arXiv:0707.1835.

25. p^k-torsion of genus two curves over GF(p^m), Math. Comp. 79 (2010), 1833–1838.

24. Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture, with D. Ghioca and T. Tucker, Inventiones Math. 171 (2008), 463–483, arXiv:0705.1954.

23. Equivalence of sparse circulants: the bipartite Ádám problem, with D. Wiedemann, submitted, arXiv:0706.1567.

22. Equivalence classes of permutation binomials up to composition with monomials, with A. Masuda, preprint.

21. On some permutation polynomials over GF(q) of the form x^rh(x^(q-1)/d), Proc. Amer. Math. Soc. 137 (2009), 2209–2216, arXiv:0707.1110.

20. Some families of permutation polynomials over finite fields, Int. J. Number Theory 4 (2008), 851–857, arXiv:0707.1111.

19. Rational functions with linear relations, with A. Masuda, Proc. Amer. Math. Soc. 136 (2008), 1403–1408, arXiv:0705.2182.

18. Permutation binomials over finite fields, with A. Masuda, Trans. Amer. Math. Soc. 361 (2009), 4169–4180, arXiv:0707.1108.

17. Nonexistence of permutation binomials of certain shapes, with A. Masuda, Electronic J. Combinatorics 14 (2007), N12, arXiv:0707.1102.

16. Polynomials with a common composite, with R. Beals and J. Wetherell, Israel J. Math. 174 (2009), 93–117, arXiv:0707.1552.

15. Exceptional covers and bijections on rational points, with R. Guralnick and T. Tucker, Internat. Math. Res. Notices 2007: article ID rnm004, 19 pages, arXiv:math/0511276.

14. Everywhere ramified towers of global function fields, with I. Duursma and B. Poonen, pp. 148–153 in: Finite Fields and Applications, Lecture Notes in Comput. Sci. 2948, Springer, 2004, arXiv:0810.2842.

13. Symplectic spreads and permutation polynomials, with S. Ball, pp. 79–88 in: Finite Fields and Applications, Lecture Notes in Comput. Sci. 2948, Springer, 2004, arXiv:0810.2839.

12. Curves of every genus with many points, II: Asymptotically good families, with N. Elkies, E. Howe, A. Kresch, B. Poonen and J. Wetherell, Duke Math. J. 122 (2004), 399–422, arXiv:math/0208060.

11. Curves of every genus with many points, I: Abelian and toric families, with A. Kresch and J. Wetherell, J. Algebra 250 (2002), 353–370, arXiv:math/9912069.

10. Incomplete character sums and a special class of permutations, with S. Cohen, H. Niederreiter and I. Shparlinski, J. Theor. Nombres Bordeaux 13 (2001), 53–63.

9. On the genera of X₀ (N), with J. Csirik and J. Wetherell, 2000, arXiv:math/0006096.

8. Bivariate factorizations connecting Dickson polynomials and Galois theory, with S. Abhyankar and S. Cohen, Trans. Amer. Math. Soc. 352 (2000), 2871–2887.

7. Factoring Dickson polynomials over finite fields, with M. Bhargava, Finite Fields Appl. 5 (1999), 103–111.

6. Bivariate factorizations via Galois theory, with application to exceptional polynomials, J. Algebra 210 (1998), 670–689.

5. A note on the discriminator, J. Number Theory 73 (1998), 122–138.

4. Cycles of Polynomial Mappings, Ph.D. thesis, Berkeley, 1996.

3. A family of exceptional polynomials in characteristic three, with H. Lenstra, pp. 209–218 in: Finite Fields and Applications, London Math. Soc. Lecture Note Ser. 233, Cambridge Univ. Press, Cambridge, 1996.

2. Take-away games, pp. 351–361 in: Games of No Chance, Math. Sci. Res. Inst. Publ. 29, Cambridge Univ. Press, 1996.

1. Polynomial mappings mod pⁿ, with D. desJardins, 1994, arXiv:math/0103046.

In preparation

4. New families of supersingular curves, and the Hall-Janko group as Galois group in characteristic 5, with N. Elkies and E. Rains.

3. Maximal curves and unramified coverings, with R. Fuhrmann, A. Garcia and F. Torres.

2. Annihilators of polynomials, with N. Kayal.

1. A bound on the number of GF(q)-points on a genus-g curve, with D. Yuen.

Michael Zieve

44.		Planar monomials in characteristic 2, with Z. Scherr, submitted, arXiv:1302.1244.
43.		Planar functions and perfect nonlinear monomials over finite fields, submitted, arXiv:1301.5004.
42.		Exceptional polynomials, pp. 229–233 in: Handbook of Finite Fields, CRC Press, 2013.
41.		Value sets of polynomials, with G. Mullen, pp. 225–229 in: Handbook of Finite Fields, CRC Press, 2013.
40.		The Mordell-Lang question for endomorphisms of semiabelian varieties, with D. Ghioca and T. Tucker, J. Théor. Nombres Bordeaux 23 (2011), 645–666.
39.		Chebyshev mappings of finite fields, with J. Rosen, Z. Scherr and B. Weiss, Amer. Math. Monthly 119 (2012), 151–155.
38.		Two questions on polynomial decomposition, with B. Wyman, Quarterly Journal of Math. (Oxford) 63 (2012), 507–511.
37.		On hyperbolic fixed points in ultrametric dynamics, with K.-O. Lindahl, p-Adic Numbers, Ultrametric Analysis and Applications 2 (2010), 232–240.
36.		An equality between two towers over cubic fields, Bull. Braz. Math. Soc., to appear, arXiv:0905.4921.
35.		Classes of permutation polynomials based on cyclotomy and an additive analogue, pp. 355–359 in: Additive Number Theory, Springer, 2010, arXiv:0810.2830.
34.		On a theorem of Carlitz, submitted, arXiv:0810.2834.
33.		Linear relations between polynomial orbits, with D. Ghioca and T. Tucker, Duke Math. J. 161 (2012), 1379–1410. arXiv:0807.3576.
32.		On Ritt's polynomial decomposition theorems, with P. Müller, submitted, arXiv:0807.3578.
31.		Uniform bounds on pre-images under quadratic dynamical systems, with X. Faber, B. Hutz, P. Ingram, R. Jones, M. Manes and T. Tucker, Math. Research Letters 16 (2009), 87–101. arXiv:0805.0441.
30.		Nonisomorphic curves that become isomorphic over extensions of coprime degrees, with D. Goldstein, R. Guralnick and E. Howe, J. Algebra 320 (2008), 2526–2558, arXiv:0801.4614.
29.		Analogues of the Jordan-Hölder theorem for transitive G-sets, with G. Kuperberg and R. Lyons, submitted, arXiv:0712.4142.
28.		Decompositions of Laurent polynomials, submitted, arXiv:0710.1902.
27.		A new family of exceptional polynomials in characteristic two, with R. Guralnick and J. Rosenberg, Annals of Math. 172 (2010), 1367–1396, arXiv:0707.1837.
26.		Polynomials with PSL(2) monodromy, with R. Guralnick, Annals of Math. 172 (2010), 1321–1365, arXiv:0707.1835.
25.		p^k-torsion of genus two curves over GF(p^m), Math. Comp. 79 (2010), 1833–1838.
24.		Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture, with D. Ghioca and T. Tucker, Inventiones Math. 171 (2008), 463–483, arXiv:0705.1954.
23.		Equivalence of sparse circulants: the bipartite Ádám problem, with D. Wiedemann, submitted, arXiv:0706.1567.
22.	Equivalence classes of permutation binomials up to composition with monomials, with A. Masuda, preprint.
21.		On some permutation polynomials over GF(q) of the form x^rh(x^(q-1)/d), Proc. Amer. Math. Soc. 137 (2009), 2209–2216, arXiv:0707.1110.
20.		Some families of permutation polynomials over finite fields, Int. J. Number Theory 4 (2008), 851–857, arXiv:0707.1111.
19.		Rational functions with linear relations, with A. Masuda, Proc. Amer. Math. Soc. 136 (2008), 1403–1408, arXiv:0705.2182.
18.		Permutation binomials over finite fields, with A. Masuda, Trans. Amer. Math. Soc. 361 (2009), 4169–4180, arXiv:0707.1108.
17.		Nonexistence of permutation binomials of certain shapes, with A. Masuda, Electronic J. Combinatorics 14 (2007), N12, arXiv:0707.1102.
16.		Polynomials with a common composite, with R. Beals and J. Wetherell, Israel J. Math. 174 (2009), 93–117, arXiv:0707.1552.
15.		Exceptional covers and bijections on rational points, with R. Guralnick and T. Tucker, Internat. Math. Res. Notices 2007: article ID rnm004, 19 pages, arXiv:math/0511276.
14.		Everywhere ramified towers of global function fields, with I. Duursma and B. Poonen, pp. 148–153 in: Finite Fields and Applications, Lecture Notes in Comput. Sci. 2948, Springer, 2004, arXiv:0810.2842.
13.		Symplectic spreads and permutation polynomials, with S. Ball, pp. 79–88 in: Finite Fields and Applications, Lecture Notes in Comput. Sci. 2948, Springer, 2004, arXiv:0810.2839.
12.		Curves of every genus with many points, II: Asymptotically good families, with N. Elkies, E. Howe, A. Kresch, B. Poonen and J. Wetherell, Duke Math. J. 122 (2004), 399–422, arXiv:math/0208060.
11.		Curves of every genus with many points, I: Abelian and toric families, with A. Kresch and J. Wetherell, J. Algebra 250 (2002), 353–370, arXiv:math/9912069.
10.		Incomplete character sums and a special class of permutations, with S. Cohen, H. Niederreiter and I. Shparlinski, J. Theor. Nombres Bordeaux 13 (2001), 53–63.
9.		On the genera of X₀ (N), with J. Csirik and J. Wetherell, 2000, arXiv:math/0006096.
8.		Bivariate factorizations connecting Dickson polynomials and Galois theory, with S. Abhyankar and S. Cohen, Trans. Amer. Math. Soc. 352 (2000), 2871–2887.
7.		Factoring Dickson polynomials over finite fields, with M. Bhargava, Finite Fields Appl. 5 (1999), 103–111.
6.		Bivariate factorizations via Galois theory, with application to exceptional polynomials, J. Algebra 210 (1998), 670–689.
5.		A note on the discriminator, J. Number Theory 73 (1998), 122–138.
4.		Cycles of Polynomial Mappings, Ph.D. thesis, Berkeley, 1996.
3.		A family of exceptional polynomials in characteristic three, with H. Lenstra, pp. 209–218 in: Finite Fields and Applications, London Math. Soc. Lecture Note Ser. 233, Cambridge Univ. Press, Cambridge, 1996.
2.		Take-away games, pp. 351–361 in: Games of No Chance, Math. Sci. Res. Inst. Publ. 29, Cambridge Univ. Press, 1996.
1.		Polynomial mappings mod pⁿ, with D. desJardins, 1994, arXiv:math/0103046.

4.	New families of supersingular curves, and the Hall-Janko group as Galois group in characteristic 5, with N. Elkies and E. Rains.
3.	Maximal curves and unramified coverings, with R. Fuhrmann, A. Garcia and F. Torres.
2.	Annihilators of polynomials, with N. Kayal.
1.	A bound on the number of GF(q)-points on a genus-g curve, with D. Yuen.