A genus is called an elliptic genus if the power series Q(z) = z/f(z) satisfies the condition
- f ′2 = 1 − 2δf2 + εf4
for constants δ and ε. (As usual, Q is the characteristic power series of the genus.)
Examples:
- δ = ε = 1, f(z) = tanh(z). This is the L-genus.
- δ = −1/8, ε = 0, f(z) = 2sinh(z/2). This is the  genus.
Read more about this topic: Genus Of A Multiplicative Sequence
Famous quotes containing the word genus:
“Methinks it would be some advantage to philosophy if men were named merely in the gross, as they are known. It would be necessary only to know the genus and perhaps the race or variety, to know the individual. We are not prepared to believe that every private soldier in a Roman army had a name of his own,—because we have not supposed that he had a character of his own.”
—Henry David Thoreau (1817–1862)