Dirichlet hyperbola method

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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[edit]

Let be the number-of-divisors function. Since , the Dirichlet hyperbola method gives us the result[1][2]

Wherer is the Euler–Mascheroni constant.

See also[edit]

References[edit]

  1. ^ "Dirichlet hyperbola method". planetmath.org. Retrieved 2018-06-12.
  2. ^ Tenenbaum, Gérald (2015-07-16). Introduction to Analytic and Probabilistic Number Theory. American Mathematical Soc. p. 44. ISBN 9780821898543.