A converse theorem for Dirichlet L-functions
Authors:
- Jerzy Kaczorowski,
- Giuseppe Molteni,
- Alberto Perelli
Abstract
It is known that the space of solutions (in a suitable class of Dirichlet series with continuation over ℂ) of the functional equation of a Dirichlet L-functions L(s, χ) has dimension ≥ 2 as soon as the conductor q of χ is at least 4. Hence the Dirichlet L-functions are not characterized by their functional equation for q ≥ 4. Here we characterize the conductors q such that for every primitive character χ (mod q), L(s, xχ) is the only solution with an Euler product in the above space. It turns out that such conductors are of the form q = 2a3bm with any square-free m coprime to 6 and finitely many a and b. © Swiss Mathematical Society.
- Record ID
- UAMff99817e9e9c450db7eef6130b014065
- Author
- Journal series
- Commentarii Mathematici Helvetici, ISSN 0010-2571
- Issue year
- 2010
- Vol
- 85
- Pages
- 463-483
- ASJC Classification
- DOI
- DOI:10.4171/CMH/202 Opening in a new tab
- Language
- (en) English
- Score (nominal)
- 0
- Score source
- journalList
- Publication indicators
- = 7; = 7; : 2010 = 1.032; : 2010 (2 years) = 1.141 - 2010 (5 years) =1.289
- Uniform Resource Identifier
- https://researchportal.amu.edu.pl/info/article/UAMff99817e9e9c450db7eef6130b014065/
- URN
urn:amu-prod:UAMff99817e9e9c450db7eef6130b014065
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or PerishOpening in a new tab system.