Hypergeometric functions and a family of algebraic curves

Let lambda is an element of Q\{0,1} and l >= 2, and denote by C (l,lambda) the nonsingular projective algebraic curve over a"e with affine equation given by yl = x(x - 1)(x - lambda) In this paper, we define Omega(C (l,lambda) ) analogous to the real periods of elliptic curves and find a relation with ordinary hypergeometric series. We also give a relation between the number of points on C (l,lambda) over a finite field and Gaussian hypergeometric series. Finally, we give an alternate proof of a result of Rouse (Ramanujan J. 12(2):197-205, 2006).