Abstract
Let q = p
r be a prime power. Let 
be a homogenous polynomial of degree d. Let 
be the hypersurface defined by 
. A natural question to ask is how to determine 
.
Recently, several algorithms were presented that calculate 
if 
is a smooth hypersurface. We would like to investigate whether these algorithms extend to singular hypersurfaces.
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Kloosterman, R. (2008). Point Counting on Singular Hypersurfaces. In: van der Poorten, A.J., Stein, A. (eds) Algorithmic Number Theory. ANTS 2008. Lecture Notes in Computer Science, vol 5011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79456-1_22
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DOI: https://doi.org/10.1007/978-3-540-79456-1_22
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