Definition:First Chebyshev Function

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Definition

The First Chebyshev Function is defined and denoted:

$\ds \map \vartheta x := \sum_{p \mathop \le x} \ln p$

where the summation extends over all prime numbers $p$ such that $p \le x$.


Also denoted as

Some sources use $\map \theta x$ rather than $\map \vartheta x$.


Source of Name

This entry was named for Pafnuty Lvovich Chebyshev.