Kronecker Limit Formula - Second Kronecker Limit Formula

Second Kronecker Limit Formula

The second Kronecker limit formula states that

E_{u,v}(\tau,1) = -2\pi\log|f(u-v\tau;\tau)q^{v^2/2}|,

where

  • u and v are real and not both integers.
  • q = e2π i τ and qa = e2π i aτ
  • p = e2π i z and pa = e2π i az

for Re(s) > 1, and is defined by analytic continuation for other values of the complex number s.

Read more about this topic:  Kronecker Limit Formula

Famous quotes containing the words limit and/or formula:

    No one who cannot limit himself has ever been able to write.
    Nicolas Boileau-Despréaux (1636–1711)

    Hidden away amongst Aschenbach’s writing was a passage directly asserting that nearly all the great things that exist owe their existence to a defiant despite: it is despite grief and anguish, despite poverty, loneliness, bodily weakness, vice and passion and a thousand inhibitions, that they have come into being at all. But this was more than an observation, it was an experience, it was positively the formula of his life and his fame, the key to his work.
    Thomas Mann (18751955)