I haven't been able to find a reference that tells what word (if a word) the L is short for.
what does the "L" in "L-function" stand for?
5
$\begingroup$
terminology
special-functions
l-functions
-
2This was asked on MathOverflow: http://mathoverflow.net/questions/21375/why-are-they-called-l-functions – 2011-02-08
1 Answers
1
From KConrad on MathOverflow:
It is not known why Dirichlet denoted his functions with an $L$. Perhaps he chose $L$ for Legendre (I am not serious). The reason may be alphabetical. Just before $L$-functions are introduced in his 1837 paper on primes in arithmetic progression (Math. Werke vol. 1, 313–342), there are certain functions $G$ and $H$, and the letters $I, J$, and $K$ may not have seemed appropriate labels for a function.
While $L(s,\chi)$ and $L(\chi,s)$ are common notations for the $L$-function of a character $\chi$, neither decorated notation is due to Dirichlet; he simply wrote different $L$-functions as $L_0, L_1, L_2,\dots$.