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4 papers
On Belyi's Theorems in Positive Characteristic
Nurdagul Anbar, Seher Tutdere
There are two types of Belyi's Theorem for curves defined over finite fields of characteristic p, namely the Wild and the Tame p-Belyi Theorems. In this paper, we discuss them in t…
Construction of Arithmetic Secret Sharing Schemes by Using Torsion Limits
Seher Tutdere, Osmanbey Uzunkol
Recent results of Cascudo, Cramer, and Xing on the construction of arithmetic secret sharing schemes are improved by using some new bounds on the torsion limits of algebraic functi…
Lower bounds on the number of rational points of Jacobians over finite fields and application to algebraic function fields in towers
Stéphane Ballet, Robert Rolland, Seher Tutdere
We give effective bounds for the class number of any algebraic function field of genus defined over a finite field. These bounds depend on the possibly partial information on t…
On the Invariants of Towers of Function Fields over Finite Fields
Florian Hess, Henning Stichtenoth, Seher Tutdere
We consider a tower of function fields F=(F_n)_{n\geq 0} over a finite field F_q and a finite extension E/F_0 such that the sequence \mathcal{E):=(EF_n)_{n\goq 0} is a tower over t…