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Everything about Prime-counting function
Function representing the number of primes less than or equal to a given number
In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. It is denoted by π(x) (unrelated to the number π). Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Prime-counting functionA 5-minute orientation
- Skim a recent paper: Improving bounds on prime counting functions by partial verification of the Riemann hypothesisInfluential work since 2022
- Pick up a classic book: Mathematical structures for computer scienceThe most-reprinted book on the subject
- Read the landmark paper: The prime-counting function and its analytic approximationsCited 21 times
- Go sideways: Prime number theoremA closely related topic
- Go sideways: Explicit formulae for L-functionsA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
The prime-counting function and its analytic approximations
A remark on a sum involving the prime counting function
Generalised prime systems with periodic integer counting function
A property of the counting function of integers with no large prime factors
On a Constant Related to the Prime Counting Function
Power spectrum of the difference between the prime-number counting function and Riemann's function: 1/f2?
The Fractal Nature of an Approximate Prime Counting Function
On the asymptotics of the element counting function in an additive arithmetic semigroup with exponential counting function of prime generators
🆕 Influential since 2022
Improving bounds on prime counting functions by partial verification of the Riemann hypothesis
On certain inequalities for the prime counting function – Part III
Exceptional biases in counting primes over function fields
Asymptotic expansions of the prime counting function
Relationship Between the Prime-Counting Function and a Unique Prime Number Sequence
📚 Books worth reading
Mathematical structures for computer scienceJudith L. Gersting · 1982
Discrete and combinatorial mathematicsRalph P. Grimaldi · 1985
Cartesian meditationsEdmund Husserl, Dorion Cairns · 1960
A concise introduction to pure mathematicsMartin Liebeck, M. W. Liebeck · 2000
Eloquent JavascriptMarijn Haverbeke · 2009
A Book of Abstract AlgebraCharles C. Pinter · 1982
Discrete mathematicsNorman Biggs · 1985
The Conspirators HierarchyJohn Coleman · 1992
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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