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Dirichlet hyperbola method

From Wikipedia, the free encyclopedia

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


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

See also


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