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A uniqueness property of general Dirichlet series
- Source :
- Journal of Number Theory. 206:123-137
- Publication Year :
- 2020
- Publisher :
- Elsevier BV, 2020.
-
Abstract
- Let $F(s)=\sum_n a_n/\lambda_n^s$ be a general Dirichlet series which is absolutely convergent on $\Re(s)>1$. Assume that $F(s)$ has an analytic continuation and satisfies a growth condition, which gives rise to certain invariants namely the degree $d_F$ and conductor $\alpha_F$. In this paper, we show that there are at most $2d_F$ general Dirichlet series with a given degree $d_F$, conductor $\alpha_F$ and residue $\rho_F$ at $s=1$. As a corollary, we get that elements in the extended Selberg class with positive Dirichlet coefficients are determined by their degree, conductor and the residue at $s=1$.<br />Comment: 11 pages
- Subjects :
- Pure mathematics
Algebra and Number Theory
Mathematics - Number Theory
Analytic continuation
010102 general mathematics
010103 numerical & computational mathematics
Mathematics::Spectral Theory
Absolute convergence
01 natural sciences
Dirichlet distribution
Conductor
symbols.namesake
Corollary
FOS: Mathematics
symbols
11M41
Number Theory (math.NT)
Uniqueness
0101 mathematics
Selberg class
General Dirichlet series
Mathematics
Subjects
Details
- ISSN :
- 0022314X
- Volume :
- 206
- Database :
- OpenAIRE
- Journal :
- Journal of Number Theory
- Accession number :
- edsair.doi.dedup.....360c67ad017e67b4573798e913f7e691