TOPICS

Taniguchi's Constant

Taniguchi's constant is defined as

 (1) (2)

(OEIS A175639), where the product is over the primes . Taking the logarithm, expand the sum about infinity, and then summing the terms gives a "closed" form as

 (3) (4)

where is the prime zeta function and the s are rational numbers given as the coefficients of in the series

 (5)

Artin's Constant, Barban's Constant, Feller-Tornier Constant, Heath-Brown-Moroz Constant, Murata's Constant, Prime Products, Prime Zeta Function, Quadratic Class Number Constant, Sarnak's Constant, Twin Primes Constant

References

Finch, S. "Class Number Theory." http://algo.inria.fr/csolve/clss.pdf. May 6, 2005.Sloane, N. J. A. Sequence A175639 in "The On-Line Encyclopedia of Integer Sequences."Taniguchi, T. "A Mean Value Theorem for the Square of Class Number Times Regulator of Quadratic Extensions." http://arxiv.org/abs/math/0410531. 3 Jul 2006.

Cite this as:

Weisstein, Eric W. "Taniguchi's Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TaniguchisConstant.html