Value sets of Lattes maps over finite fields

Date

2015-07-13

Author

Küçüksakallı, Ömer

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http://www.skidmore.edu/fq12/talks.php
https://hdl.handle.net/11511/72581

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Value sets of Lattes maps over finite fields Küçüksakallı, Ömer (Elsevier BV, 2014-10-01) We give an alternative computation of the value sets of Dickson polynomials over finite fields by using a singular cubic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic case. We determine the value sets of Lattes maps over finite fields which are rational functions induced by isogenies of elliptic curves with complex multiplication.
Value sets of bivariate Chebyshev maps over finite fields Küçüksakallı, Ömer (2015-11-01) We determine the cardinality of the value sets of bivariate Chebyshev maps over finite fields. We achieve this using the dynamical properties of these maps and the algebraic expressions of their fixed points in terms of roots of unity.
Value sets of bivariate folding polynomials over finite fields Küçüksakallı, Ömer (2018-11-01) We find the cardinality of the value sets of polynomial maps associated with simple complex Lie algebras B-2 and G(2) over finite fields. We achieve this by using a characterization of their fixed points in terms of sums of roots of unity.
Value sets of folding polynomials over finite fields Küçüksakallı, Ömer (2019-01-01) Let k be a positive integer that is relatively prime to the order of the Weyl group of a semisimple complex Lie algebra g. We find the cardinality of the value sets of the folding polynomials P-g(k)(x) is an element of Z[x] of arbitrary rank n >= 1, over finite fields. We achieve this by using a characterization of their fixed points in terms of exponential sums.
Boundary values of vector valued hardy classes of harmonic and analytic functions on the unit disc Sümergen, Zeynep Deniz; Aytuna, Aydın; Department of Mathematics (1995)

Citation Formats

Ö. Küçüksakallı, “Value sets of Lattes maps over finite fields,” 2015, Accessed: 00, 2021. [Online]. Available: http://www.skidmore.edu/fq12/talks.php.