Dwork family

In algebraic geometry, a Dwork family is a one-parameter family of hypersurfaces depending on an integer n, studied by Bernard Dwork. Originally considered by Dwork in the context of local zeta-functions, such families have been shown to have relationships with mirror symmetry and extensions of the modularity theorem.

Definition
The Dwork family is given by the equations


 * $$ x_1^n + x_2^n +\cdots +x_n^n = -n\lambda x_1x_2\cdots x_n \, ,$$

for all $$ n\ge 1$$.