Premium
PRIME NUMBER THEOREM EQUIVALENCES AND NON‐EQUIVALENCES
Author(s) -
Diamond Harold G.,
Zhang WenBin
Publication year - 2017
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579317000201
Subject(s) - mathematics , prime (order theory) , prime number , multiplicative number theory , prime number theorem , pure mathematics , discrete mathematics , algebra over a field , prime factor , combinatorics
There are several formulas in classical prime number theory that are said to be “equivalent” to the Prime Number Theorem. For Beurling generalized numbers, not all such implications hold unconditionally. Here we investigate conditions under which the Beurling version of these relations do or do not hold.