ERIC Number: EJ799529
Record Type: Journal
Publication Date: 2008-Jul
Reference Count: 2
A Generalization of the Prime Number Theorem
Bruckman, Paul S.
International Journal of Mathematical Education in Science and Technology, v39 n5 p631-635 Jul 2008
In this article, the author begins with the prime number theorem (PNT), and then develops this into a more general theorem, of which many well-known number theoretic results are special cases, including PNT. He arrives at an asymptotic relation that allows the replacement of certain discrete sums involving primes into corresponding differentiable integral functions. The author defines the logarithmic integral as the "Eulerian" function Li(N), having a lower limit of 2, instead of the lower limit of 0 that defines the "American" logarithmic integral function li(N).
Descriptors: Numbers, Generalization, Mathematics Instruction, Generalizability Theory, Equations (Mathematics)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Authoring Institution: N/A