Abstract
We revisit class number formulas, “ s = 0 ”-version of Kroneckerʼs limit formulas and Chowla–Selberg formulas for number fields, based on the theory at s = 0 of zeta functions. The main tool in our investigation is Heckeʼs formula (Corollary to Theorem 1), which represents the zeta function of an algebraic number field K by the integral of Epsteinʼs zeta series summed over Z r . The formulas are derived without residue computations of zeta functions. Theorem 2 for class numbers is quite useful. For Chowla–Selberg formulas, the second gamma function with a character is utilized.
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