Sembolik Hesaplama İstanbul Toplantıları Seminerleri
Divisibility of L-Polynomials for a Family of Artin-Schreier Curves
Emrah Sercan Yılmaz
Atılım University, Türkiye
In this talk we consider the curves $C_k^{(p,a)}: y^p-y = x^{p^k+1} + ax$ defined over $\mathbb F_p$ and give a positive answer to a conjecture about a divisibility condition on $L$-polynomials of the curves $C_k^{(p,a)}$. Our proof involves finding an exact formula for the number of $\mathbb F_{p^n}$-rational points on $C_k^{(p,a)}$ for all $n$, and uses a result we proved elsewhere about the number of rational points on supersingular curves.
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Meeting ID: 645 3608 0348 Password: scimtalk
