Zobrazeno 1 - 10
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pro vyhledávání: '"Zieve, Michael E."'
Autor:
Neftin, Danny, Zieve, Michael E.
The combination of this paper and its companion complete the classification of monodromy groups of indecomposable coverings of complex curves $f:X\rightarrow \mathbb P^1$ of sufficiently large degree in comparison to the genus of $X$. In this paper w
Externí odkaz:
http://arxiv.org/abs/2403.17168
Autor:
Neftin, Danny, Zieve, Michael E.
For each nonnegative integer $g$, we classify the ramification types and monodromy groups of indecomposable coverings of complex curves $f: X\to Y$ where $X$ has genus $g$, under the hypothesis that $n:=\deg(f)$ is sufficiently large and the monodrom
Externí odkaz:
http://arxiv.org/abs/2403.17167
Autor:
Ding, Zhiguo, Zieve, Michael E.
For each odd prime power q, and each integer k, we determine the sum of the k-th powers of all elements x in F_q for which both x and x+1 are squares in F_q^*. We also solve the analogous problem when one or both of x and x+1 is a nonsquare. We use t
Externí odkaz:
http://arxiv.org/abs/2309.14979
Autor:
Ding, Zhiguo, Zieve, Michael E.
If S is a set of q+2 points in P^2(F_q) such that some point of S is not on any line containing two other points of S, then in suitable coordinates S has the form S_f:={(c:f(c):1) : c in F_q} U {(1:0:0),(0:1:0)} for some f(X) in F_q[X]. Let T be a su
Externí odkaz:
http://arxiv.org/abs/2309.10866
Autor:
Ding, Zhiguo, Zieve, Michael E.
We determine all permutations in two large classes of polynomials over finite fields, where the construction of the polynomials in each class involves the denominators of a class of rational functions generalizing the classical Redei functions. Our r
Externí odkaz:
http://arxiv.org/abs/2305.06322
Autor:
Ding, Zhiguo, Zieve, Michael E.
We determine the roots in F_{q^3} of the polynomial X^{2q^k+1} + X + c for each positive integer k and each c in F_q, where q is a power of 2. We introduce a new approach for this type of question, and we obtain results which are more explicit than t
Externí odkaz:
http://arxiv.org/abs/2302.13478
Autor:
Zieve, Michael E.
We show that all of the "new" permutation polynomials in the recent paper arXiv:2207.13335 (H. Song et al.) are in fact known. We also present a new type of question in this area.
Comment: 3 pages
Comment: 3 pages
Externí odkaz:
http://arxiv.org/abs/2208.01601
Autor:
Ding, Zhiguo, Zieve, Michael E.
We determine all permutation polynomials over F_{q^2} of the form X^r A(X^{q-1}) where, for some Q which is a power of the characteristic of F_q, the integer r is congruent to Q+1 (mod q+1) and all terms of A(X) have degrees in {0, 1, Q, Q+1}. We the
Externí odkaz:
http://arxiv.org/abs/2203.04216
Autor:
Ding, Zhiguo, Zieve, Michael E.
Publikováno v:
In Finite Fields and Their Applications March 2024 95
Autor:
Ding, Zhiguo, Zieve, Michael E.
Recently Lima and Campello de Souza introduced a new class of rational functions over odd-order finite fields, and explained their potential usefulness in cryptography. We show that these new functions are conjugate to the classical family of Redei r
Externí odkaz:
http://arxiv.org/abs/2103.08128