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## Zieve, Michael E.

Compute Distance To:
 Author ID: zieve.michael-e Published as: Zieve, M.; Zieve, Michael; Zieve, Michael E.
 Documents Indexed: 38 Publications since 1996 Reviewing Activity: 2 Reviews
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#### Co-Authors

 9 single-authored 6 Tucker, Thomas John 4 Guralnick, Robert Michael 4 Scherr, Zachary 3 Ghioca, Dragos 3 Masuda, Ariane M. 3 Wetherell, Joseph L. 2 Cohen, Stephen D. 2 Howe, Everett W. 2 Kresch, Andrew 2 Poonen, Bjorn 1 Abhyankar, Shreeram Shankar 1 Ball, Simeon 1 Beals, Robert M. 1 Bhargava, Manjul 1 Duursma, Iwan Maynard 1 Elkies, Noam David 1 Faber, Xander 1 Goldstein, Daniel E. 1 Hutz, Benjamin 1 Ingram, Patrick 1 Jones, Rafe 1 Krieger, Holly 1 Kyureghyan, Gohar M. 1 Lenstra, Hendrik W. jun. 1 Levin, Aaron 1 Lindahl, Karl-Olof 1 Manes, Michelle 1 Müller, Peter 1 Niederreiter, Harald 1 Rosen, Julian 1 Rosenberg, Joel 1 Shparlinski, Igor E. 1 Voloch, José Felipe 1 Weiss, Benjamin L. 1 Wyman, Brian K. 1 Yasufuku, Yu
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#### Serials

 3 Journal of Algebra 2 Duke Mathematical Journal 2 Proceedings of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 Journal de Théorie des Nombres de Bordeaux 2 Mathematical Research Letters 2 Annals of Mathematics. Second Series 2 International Journal of Number Theory 1 American Mathematical Monthly 1 Israel Journal of Mathematics 1 Mathematics of Computation 1 Inventiones Mathematicae 1 Journal of Number Theory 1 Pacific Journal of Mathematics 1 IMRN. International Mathematics Research Notices 1 Designs, Codes and Cryptography 1 Journal of Algebraic Combinatorics 1 Finite Fields and their Applications 1 The Electronic Journal of Combinatorics 1 Journal of Group Theory 1 Annals of Combinatorics 1 The Quarterly Journal of Mathematics 1 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications
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#### Fields

 27 Number theory (11-XX) 13 Algebraic geometry (14-XX) 8 Field theory and polynomials (12-XX) 6 Dynamical systems and ergodic theory (37-XX) 4 Geometry (51-XX) 3 Combinatorics (05-XX) 1 Commutative algebra (13-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Computer science (68-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX)

#### Citations contained in zbMATH Open

35 Publications have been cited 322 times in 227 Documents Cited by Year
On some permutation polynomials over $$\mathbb {F}_q$$ of the form $$x^r h(x^{(q-1)/d})$$. Zbl 1228.11177
Zieve, Michael E.
2009
Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture. Zbl 1191.14027
Ghioca, Dragos; Tucker, Thomas J.; Zieve, Michael E.
2008
Permutation binomials over finite fields. Zbl 1239.11139
Masuda, Ariane M.; Zieve, Michael E.
2009
Some families of permutation polynomials over finite fields. Zbl 1204.11180
Zieve, Michael E.
2008
Classes of permutation polynomials based on cyclotomy and an additive analogue. Zbl 1261.11081
Zieve, Michael E.
2010
Factoring Dickson polynomials over finite fields. Zbl 0929.11060
Bhargava, Manjul; Zieve, Michael E.
1999
Linear relations between polynomial orbits. Zbl 1267.37043
Ghioca, Dragos; Tucker, Thomas J.; Zieve, Michael E.
2012
Planar functions and perfect nonlinear monomials over finite fields. Zbl 1314.51003
Zieve, Michael E.
2015
Exceptional covers and bijections on rational points. Zbl 1127.14023
Guralnick, Robert M.; Tucker, Thomas J.; Zieve, Michael E.
2007
Symplectic spreads and permutation polynomials. Zbl 1066.51005
Ball, Simeon; Zieve, Michael
2004
A family of exceptional polynomials in characteristic three. Zbl 0871.11087
Lenstra, H. W. jun.; Zieve, M.
1996
Some planar monomials in characteristic 2. Zbl 1310.51006
Scherr, Zachary; Zieve, Michael E.
2014
Permutation polynomials of the form $$X + \gamma \mathrm{Tr}(X^k)$$. Zbl 1382.11090
Kyureghyan, Gohar; Zieve, Michael
2016
Polynomials with $$\text{PSL}(2)$$ monodromy. Zbl 1214.12003
Guralnick, Robert M.; Zieve, Michael E.
2010
Bivariate factorizations connecting Dickson polynomials and Galois theory. Zbl 0989.12001
Abhyankar, Shreeram S.; Cohen, Stephen D.; Zieve, Michael E.
2000
The Mordell-Lang question for endomorphisms of semiabelian varieties. Zbl 1256.14046
Ghioca, Dragos; Tucker, Thomas; Zieve, Michael E.
2011
A new family of exceptional polynomials in characteristic two. Zbl 1214.12002
Guralnick, Robert M.; Rosenberg, Joel; Zieve, Michael E.
2010
Curves of every genus with many points. II: Asymptotically good families. Zbl 1072.11041
Elkies, Noam D.; Howe, Everett W.; Kresch, Andrew; Poonen, Bjorn; Wetherell, Joseph L.; Zieve, Michael E.
2004
Low-degree planar monomials in characteristic two. Zbl 1343.51005
Müller, Peter; Zieve, Michael E.
2015
Curves of every genus with many points. I: Abelian and toric families. Zbl 1062.14027
Kresch, Andrew; Wetherell, Joseph L.; Zieve, Michael E.
2002
Rational points on some Fermat curves and surfaces over finite fields. Zbl 1286.11099
Voloch, José Felipe; Zieve, Michael E.
2014
Uniform bounds on pre-images under quadratic dynamical systems. Zbl 1222.11086
Faber, Xander; Hutz, Benjamin; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Tucker, Thomas J.; Zieve, Michael E.
2009
A note on the discriminator. Zbl 0924.11017
Zieve, Michael
1998
Uniform boundedness of $$S$$-units in arithmetic dynamics. Zbl 1403.37102
Krieger, Holly; Levin, Aaron; Scherr, Zachary; Tucker, Thomas; Yasufuku, Yu; Zieve, Michael E.
2015
Polynomials with a common composite. Zbl 1195.12002
Beals, Robert M.; Wetherell, Joseph L.; Zieve, Michael E.
2009
Incomplete character sums and a special class of permutations. Zbl 1065.11097
Cohen, S. D.; Niederreiter, H.; Shparlinski, I. E.; Zieve, M.
2001
Bivariate factorizations via Galois theory, with application to exceptional polynomials. Zbl 0922.12010
Zieve, Michael
1998
Take-away games. Zbl 0872.90150
Zieve, Michael
1997
On a theorem of Carlitz. Zbl 1311.11112
Zieve, Michael E.
2014
Chebyshev mappings of finite fields. Zbl 1245.11117
Rosen, Julian; Scherr, Zachary; Weiss, Benjamin; Zieve, Michael E.
2012
Nonisomorphic curves that become isomorphic over extensions of coprime degrees. Zbl 1160.14020
Goldstein, Daniel; Guralnick, Robert M.; Howe, Everett W.; Zieve, Michael E.
2008
Separated Belyi maps. Zbl 1327.14161
Scherr, Zachary; Zieve, Michael E.
2014
On hyperbolic fixed points in ultrametric dynamics. Zbl 1250.37035
Lindahl, Karl-Olof; Zieve, Michael
2010
$$p^k$$-torsion of genus two curves over $$\mathbb F_{p^m}$$. Zbl 1197.14028
Zieve, Michael E.
2010
Nonexistence of permutation binomials of certain shapes. Zbl 1162.11396
Masuda, Ariane M.; Zieve, Michael E.
2007
Permutation polynomials of the form $$X + \gamma \mathrm{Tr}(X^k)$$. Zbl 1382.11090
Kyureghyan, Gohar; Zieve, Michael
2016
Planar functions and perfect nonlinear monomials over finite fields. Zbl 1314.51003
Zieve, Michael E.
2015
Low-degree planar monomials in characteristic two. Zbl 1343.51005
Müller, Peter; Zieve, Michael E.
2015
Uniform boundedness of $$S$$-units in arithmetic dynamics. Zbl 1403.37102
Krieger, Holly; Levin, Aaron; Scherr, Zachary; Tucker, Thomas; Yasufuku, Yu; Zieve, Michael E.
2015
Some planar monomials in characteristic 2. Zbl 1310.51006
Scherr, Zachary; Zieve, Michael E.
2014
Rational points on some Fermat curves and surfaces over finite fields. Zbl 1286.11099
Voloch, José Felipe; Zieve, Michael E.
2014
On a theorem of Carlitz. Zbl 1311.11112
Zieve, Michael E.
2014
Separated Belyi maps. Zbl 1327.14161
Scherr, Zachary; Zieve, Michael E.
2014
Linear relations between polynomial orbits. Zbl 1267.37043
Ghioca, Dragos; Tucker, Thomas J.; Zieve, Michael E.
2012
Chebyshev mappings of finite fields. Zbl 1245.11117
Rosen, Julian; Scherr, Zachary; Weiss, Benjamin; Zieve, Michael E.
2012
The Mordell-Lang question for endomorphisms of semiabelian varieties. Zbl 1256.14046
Ghioca, Dragos; Tucker, Thomas; Zieve, Michael E.
2011
Classes of permutation polynomials based on cyclotomy and an additive analogue. Zbl 1261.11081
Zieve, Michael E.
2010
Polynomials with $$\text{PSL}(2)$$ monodromy. Zbl 1214.12003
Guralnick, Robert M.; Zieve, Michael E.
2010
A new family of exceptional polynomials in characteristic two. Zbl 1214.12002
Guralnick, Robert M.; Rosenberg, Joel; Zieve, Michael E.
2010
On hyperbolic fixed points in ultrametric dynamics. Zbl 1250.37035
Lindahl, Karl-Olof; Zieve, Michael
2010
$$p^k$$-torsion of genus two curves over $$\mathbb F_{p^m}$$. Zbl 1197.14028
Zieve, Michael E.
2010
On some permutation polynomials over $$\mathbb {F}_q$$ of the form $$x^r h(x^{(q-1)/d})$$. Zbl 1228.11177
Zieve, Michael E.
2009
Permutation binomials over finite fields. Zbl 1239.11139
Masuda, Ariane M.; Zieve, Michael E.
2009
Uniform bounds on pre-images under quadratic dynamical systems. Zbl 1222.11086
Faber, Xander; Hutz, Benjamin; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Tucker, Thomas J.; Zieve, Michael E.
2009
Polynomials with a common composite. Zbl 1195.12002
Beals, Robert M.; Wetherell, Joseph L.; Zieve, Michael E.
2009
Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture. Zbl 1191.14027
Ghioca, Dragos; Tucker, Thomas J.; Zieve, Michael E.
2008
Some families of permutation polynomials over finite fields. Zbl 1204.11180
Zieve, Michael E.
2008
Nonisomorphic curves that become isomorphic over extensions of coprime degrees. Zbl 1160.14020
Goldstein, Daniel; Guralnick, Robert M.; Howe, Everett W.; Zieve, Michael E.
2008
Exceptional covers and bijections on rational points. Zbl 1127.14023
Guralnick, Robert M.; Tucker, Thomas J.; Zieve, Michael E.
2007
Nonexistence of permutation binomials of certain shapes. Zbl 1162.11396
Masuda, Ariane M.; Zieve, Michael E.
2007
Symplectic spreads and permutation polynomials. Zbl 1066.51005
Ball, Simeon; Zieve, Michael
2004
Curves of every genus with many points. II: Asymptotically good families. Zbl 1072.11041
Elkies, Noam D.; Howe, Everett W.; Kresch, Andrew; Poonen, Bjorn; Wetherell, Joseph L.; Zieve, Michael E.
2004
Curves of every genus with many points. I: Abelian and toric families. Zbl 1062.14027
Kresch, Andrew; Wetherell, Joseph L.; Zieve, Michael E.
2002
Incomplete character sums and a special class of permutations. Zbl 1065.11097
Cohen, S. D.; Niederreiter, H.; Shparlinski, I. E.; Zieve, M.
2001
Bivariate factorizations connecting Dickson polynomials and Galois theory. Zbl 0989.12001
Abhyankar, Shreeram S.; Cohen, Stephen D.; Zieve, Michael E.
2000
Factoring Dickson polynomials over finite fields. Zbl 0929.11060
Bhargava, Manjul; Zieve, Michael E.
1999
A note on the discriminator. Zbl 0924.11017
Zieve, Michael
1998
Bivariate factorizations via Galois theory, with application to exceptional polynomials. Zbl 0922.12010
Zieve, Michael
1998
Take-away games. Zbl 0872.90150
Zieve, Michael
1997
A family of exceptional polynomials in characteristic three. Zbl 0871.11087
Lenstra, H. W. jun.; Zieve, M.
1996
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#### Cited by 271 Authors

 12 Bartoli, Daniele 12 Ghioca, Dragos 12 Zieve, Michael E. 11 Hou, Xiang-Dong 11 Tucker, Thomas John 11 Wang, Qiang (Steven) 11 Zeng, Xiangyong 10 Li, Kangquan 10 Qu, Longjiang 8 Helleseth, Tor 7 Ding, Cunsheng 7 Li, Nian 7 Tu, Ziran 6 Ostafe, Alina 6 Shparlinski, Igor E. 5 Yuan, Pingzhi 4 Cao, Xiwang 4 Hu, Lei 4 Li, Chao 4 Li, Chunlei 4 Schmidt, Kai-Uwe 4 Timpanella, Marco 4 Zha, Zhengbang 4 Zhou, Yue 3 Akbary, Amir 3 Benedetto, Robert L. 3 Hong, Shaofang 3 Hutz, Benjamin 3 Jones, Rafe 3 Liao, Lingmin 3 Lin, Dongdai 3 Mesnager, Sihem 3 Moree, Pieter 3 Wu, Baofeng 3 Wu, Gaofei 3 Yucas, Joseph L. 3 Zheng, Yanbin 2 Abhyankar, Shreeram Shankar 2 Caullery, Florian 2 Chen, Xi 2 Elkies, Noam David 2 Evans, Ronald J. 2 Fan, Ai Hua 2 Fan, Shilei 2 Feng, Tao 2 Feng, Xiutao 2 Ferraguti, Andrea 2 Fitzgerald, Robert W. 2 Fried, Michael David 2 Ge, Gennian 2 Giulietti, Massimo 2 Gupta, Rohit K. 2 Hidalgo, Rubén Antonio 2 Howe, Everett W. 2 Juul, Jamie 2 Kan, Haibin 2 Kim, Kwang Ho 2 Kresch, Andrew 2 Kurlberg, Pär 2 Kyureghyan, Gohar M. 2 Larsson, Urban 2 Li, Lisha 2 Li, Shuxing 2 Luca, Florian 2 Marcos, José E. 2 Micheli, Giacomo 2 Möller, Florian 2 Müller, Peter 2 Niederreiter, Harald 2 Peng, Jie 2 Pott, Alexander 2 Qin, Xiao’er 2 Quoos, Luciane 2 Rybalkin, M. A. 2 Sha, Min 2 Silverman, Joseph Hillel 2 Stichtenoth, Henning 2 Tosun, Cemile 2 Tuxanidy, Aleksandr 2 van Veen, Mark P. 2 Wang, Mingxi 2 Wetherell, Joseph L. 2 Winterhof, Arne 2 Xu, Guangkui 2 Zhang, Yuqing 2 Zheng, Lijing 1 Abdukhalikov, Kanat S. 1 Akbal, Yıldırım 1 Alaca, Şaban 1 Anbar, Nurdagül 1 Aslan, Ersin 1 Aubry, Yves 1 Ayad, Mohamed 1 Bai, Tao 1 Bavula, Vladimir V. 1 Beelen, Pieter Hendrik Turdus 1 Belghaba, Kacem 1 Bell, Jason P. 1 Bhargava, Manjul 1 Bisson, Gaetan ...and 171 more Authors
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#### Cited in 60 Serials

 71 Finite Fields and their Applications 16 Journal of Number Theory 13 Cryptography and Communications 11 Designs, Codes and Cryptography 8 Journal of Algebra 7 Discrete Mathematics 6 Transactions of the American Mathematical Society 6 International Journal of Number Theory 4 Journal of Combinatorial Theory. Series A 4 Proceedings of the American Mathematical Society 4 Journal of Algebraic Combinatorics 3 Acta Arithmetica 3 Advances in Mathematics 3 Duke Mathematical Journal 3 Mathematische Annalen 3 Ergodic Theory and Dynamical Systems 3 Bulletin of the American Mathematical Society. New Series 3 Applicable Algebra in Engineering, Communication and Computing 2 Bulletin of the Australian Mathematical Society 2 Communications in Algebra 2 Discrete Applied Mathematics 2 Journal of Pure and Applied Algebra 2 Monatshefte für Mathematik 2 SIAM Journal on Discrete Mathematics 2 Journal of Mathematical Sciences (New York) 2 Discrete and Continuous Dynamical Systems 2 Journal of Integer Sequences 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Central European Journal of Mathematics 2 Journal of Algebra and its Applications 2 Science China. Mathematics 1 Journal of Mathematical Analysis and Applications 1 Applied Mathematics and Computation 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Functiones et Approximatio. Commentarii Mathematici 1 Geometriae Dedicata 1 Glasgow Mathematical Journal 1 Illinois Journal of Mathematics 1 Inventiones Mathematicae 1 Manuscripta Mathematica 1 Mathematische Zeitschrift 1 Michigan Mathematical Journal 1 Theoretical Computer Science 1 Journal of Symbolic Computation 1 Forum Mathematicum 1 International Journal of Foundations of Computer Science 1 Expositiones Mathematicae 1 New Zealand Journal of Mathematics 1 Journal de Théorie des Nombres de Bordeaux 1 Annals of Combinatorics 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Advances in Mathematics of Communications 1 Algebra & Number Theory 1 Journal of Statistical Theory and Practice 1 São Paulo Journal of Mathematical Sciences 1 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 1 Diskretnyĭ Analiz i Issledovanie Operatsiĭ 1 Moscow Journal of Combinatorics and Number Theory 1 Annales Mathématiques du Québec
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#### Cited in 22 Fields

 187 Number theory (11-XX) 48 Algebraic geometry (14-XX) 43 Dynamical systems and ergodic theory (37-XX) 31 Combinatorics (05-XX) 30 Field theory and polynomials (12-XX) 21 Information and communication theory, circuits (94-XX) 15 Geometry (51-XX) 8 Group theory and generalizations (20-XX) 7 Commutative algebra (13-XX) 3 Computer science (68-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Functions of a complex variable (30-XX) 2 Difference and functional equations (39-XX) 2 Numerical analysis (65-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX) 1 Convex and discrete geometry (52-XX)