scholarly journals The second largest number of points on plane curves over finite fields

2018 ◽  
Vol 49 ◽  
pp. 80-93 ◽  
Author(s):  
Masaaki Homma ◽  
Seon Jeong Kim
Keyword(s):  
Finite Fields ◽  
Plane Curves ◽  
Curves Over Finite Fields

scholarly journals Sharp Bertini Theorem for Plane Curves over Finite Fields

2019 ◽  
Vol 62 (02) ◽  
pp. 223-230 ◽  
Author(s):  
Shamil Asgarli
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Plane Curve ◽  
Plane Curves ◽  
Smooth Plane ◽  
Curves Over Finite Fields

AbstractWe prove that if $C$ is a reflexive smooth plane curve of degree $d$ defined over a finite field $\mathbb{F}_{q}$ with $d\leqslant q+1$ , then there is an $\mathbb{F}_{q}$ -line $L$ that intersects $C$ transversely. We also prove the same result for non-reflexive curves of degree $p+1$ and $2p+1$ when $q=p^{r}$ .

scholarly journals Fluctuations in the number of points on smooth plane curves over finite fields

2010 ◽  
Vol 130 (11) ◽  
pp. 2528-2541 ◽  
Author(s):  
Alina Bucur ◽  
Chantal David ◽  
Brooke Feigon ◽  
Matilde Lalín
Keyword(s):  
Finite Fields ◽  
Plane Curves ◽  
Smooth Plane ◽  
Curves Over Finite Fields

scholarly journals Distributions of Traces of Frobenius for Smooth Plane Curves Over Finite Fields

2017 ◽  
Vol 28 (1) ◽  
pp. 39-48
Author(s):  
Reynald Lercier ◽  
Christophe Ritzenthaler ◽  
Florent Rovetta ◽  
Jeroen Sijsling ◽  
Benjamin Smith
Keyword(s):  
Finite Fields ◽  
Plane Curves ◽  
Smooth Plane ◽  
Curves Over Finite Fields

scholarly journals Primes in short intervals on curves over finite fields

2018 ◽  
Vol 374 (1-2) ◽  
pp. 447-474 ◽  
Author(s):  
Efrat Bank ◽  
Tyler Foster
Keyword(s):  
Finite Fields ◽  
Short Intervals ◽  
Curves Over Finite Fields
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