High-Power Analogues of the Turán-Kubilius Inequality, and an Application to Number Theory Journal Article uri icon



  • An arithmetic function ƒ(n) is said to be additive if it satisfies ƒ(ab) = ƒ(a) + ƒ(b) whenever a and b are coprime integers. For such a function we defineA standard form of the Turán-Kubilius inequality states that(1)holds for some absolute constant c1, uniformly for all complex-valued additive arithmetic functions ƒ (n), and real x ≧ 2. An inequality of this type was first established by Turán [11], [12] subject to some side conditions upon the size of │ƒ(pm)│. For the general inequality we refer to [10].This inequality, and more recently its dual, have been applied many times to the study of arithmetic functions. For an overview of some applications we refer to [2]; a complete catalogue of the applications of the inequality (1) would already be very large. For some applications of the dual of (1) see [3], [4], and [1].;

publication date

  • April 1, 1980

has restriction

  • bronze

Date in CU Experts

  • September 18, 2013 5:23 AM

Full Author List

  • Elliott PDTA

author count

  • 1

Other Profiles

International Standard Serial Number (ISSN)

  • 0008-414X

Electronic International Standard Serial Number (EISSN)

  • 1496-4279

Additional Document Info

start page

  • 893

end page

  • 907


  • 32


  • 4