## The Annals of Mathematical Statistics

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

### On the Unimodality of $L$ Functions

#### 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

**Permanent link to this document**

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**

links.jstor.org

#### Citation

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