Tau function

Tau function may refer to:

• Ramanujan tau function, giving the Fourier coefficients of the Ramanujan modular form.
• Divisor function, an arithmetic function giving the number of divisors of an integer.

Tau function is represented by 'τ' and its value is given by: τ(p^k)=(k+1) where p is prime. So; τ(p)=2 where p is prime. Example: τ(100)=τ(2^2)*τ(5^2) , because τ is a multiplicative function

           =(2+1)(2+1)
           =9 

Thus there are 9 positive divisors of 100.

• tau function (representation theory) in the representation theory of affine Lie algebras and soliton equations.