The Annals of Mathematical Statistics

On the Unimodality of $L$ Functions

Stephen James Wolfe

Abstract

It is shown that an $L$ function is unimodal if its Levy spectral function has support on $(-\infty, 0\rbrack$ or on $\lbrack 0, \infty)$, and that this implies that every $L$ function is the convolution of at most two unimodal $L$ functions. Other results concerning the unimodality of $L$ functions and other infinitely divisible distribution functions are also obtained.

Article information

Source
Ann. Math. Statist., Volume 42, Number 3 (1971), 912-918.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177693320

Digital Object Identifier
doi:10.1214/aoms/1177693320

Mathematical Reviews number (MathSciNet)
MR278357

Zentralblatt MATH identifier
0219.60026

JSTOR
Wolfe, Stephen James. On the Unimodality of $L$ Functions. Ann. Math. Statist. 42 (1971), no. 3, 912--918. doi:10.1214/aoms/1177693320. https://projecteuclid.org/euclid.aoms/1177693320