In number theory, the Dirichlet hyperbola method is a technique to evaluate the sum

where are multiplicative functions with , where is the Dirichlet convolution. It uses the fact that

Uses

Let be the number-of-divisors function. Since , the Dirichlet hyperbola method gives us the result[1]

Wherer is the Euler–Mascheroni constant.

See also

References

  1. Tenenbaum, Gérald (2015-07-16). Introduction to Analytic and Probabilistic Number Theory. American Mathematical Soc. p. 44. ISBN 9780821898543.
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