non-multiplicative function
In number theory, a non-multiplicative function is an arithmetic function which is not multiplicative.
Examples
Some examples of a non-multiplicative functions are the arithmetic functions:
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- the number of ways that can be expressed as the sum of four squares of nonnegative integers, where we distinguish between different orders of the summands. For example:
hence
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The partition function - the number of ordered representations of as a sum of positive integers. For instance:
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The Mangoldt function . and for example:
We would think that for some multiplicativity of would be true as in:
but we have to write:
Title | non-multiplicative function |
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Canonical name | NonmultiplicativeFunction |
Date of creation | 2013-03-22 12:47:04 |
Last modified on | 2013-03-22 12:47:04 |
Owner | Mathprof (13753) |
Last modified by | Mathprof (13753) |
Numerical id | 16 |
Author | Mathprof (13753) |
Entry type | Example |
Classification | msc 11A25 |
Related topic | PartitionFunction2 |
Defines | partition function |