Mertens function
E992321
UNEXPLORED
The Mertens function is an arithmetic function in number theory defined as the cumulative sum of the Möbius function, playing a key role in the study of the distribution of prime numbers and the Riemann Hypothesis.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Mertens function canonical | 4 |
How this entity was disambiguated
This entity first appeared as the object of triple T12597192 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Mertens function Context triple: [Mertens’ theorems, relatedTo, Mertens function]
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A.
Möbius function
The Möbius function is a multiplicative arithmetic function in number theory that assigns values based on the prime factorization of integers and plays a central role in inversion formulas and the study of prime distribution.
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B.
Liouville function
The Liouville function is a completely multiplicative arithmetic function that assigns values based on the parity of the total number of prime factors of an integer, playing a key role in analytic number theory and the study of prime distribution.
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C.
Riemann zeta function
The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
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D.
Chebyshev functions
Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
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E.
Ramanujan’s sum
Ramanujan’s sum is a number-theoretic function introduced by Srinivasa Ramanujan, expressing certain periodic arithmetic functions as finite trigonometric sums over primitive roots of unity.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Mertens function Target entity description: The Mertens function is an arithmetic function in number theory defined as the cumulative sum of the Möbius function, playing a key role in the study of the distribution of prime numbers and the Riemann Hypothesis.
-
A.
Möbius function
The Möbius function is a multiplicative arithmetic function in number theory that assigns values based on the prime factorization of integers and plays a central role in inversion formulas and the study of prime distribution.
-
B.
Liouville function
The Liouville function is a completely multiplicative arithmetic function that assigns values based on the parity of the total number of prime factors of an integer, playing a key role in analytic number theory and the study of prime distribution.
-
C.
Riemann zeta function
The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
-
D.
Chebyshev functions
Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
-
E.
Ramanujan’s sum
Ramanujan’s sum is a number-theoretic function introduced by Srinivasa Ramanujan, expressing certain periodic arithmetic functions as finite trigonometric sums over primitive roots of unity.
- F. None of above. chosen
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.