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

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