# Degree 1 elements of the Selberg class

```@article{Soundararajan2003Degree1E,
title={Degree 1 elements of the Selberg class},
author={Kannan Soundararajan},
journal={Expositiones Mathematicae},
year={2003},
volume={23},
pages={65-70}
}```
Strong Multiplicity One for the Selberg Class
Abstract We investigate the problem of determining elements in the Selberg class by means of their Dirichlet series coefficients at primes.
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## References

SHOWING 1-8 OF 8 REFERENCES
On the structure of the Selberg class, I: 0≤d≤1
• Mathematics
• 1999
The Selberg class S is a rather general class of Dirichlet series with functional equation and Euler product and can be regarded as an axiomatic model for the global L-functions arising from number
On the Selberg class of Dirichlet series: small degrees
• Mathematics
• 1993
In the study of Dirichlet series with arithmetic signi cance there has appeared (through the study of known examples) certain expectations, namely (i) if a functional equation and Euler product
The Theory of the Riemann Zeta-Function
• Mathematics
• 1987
The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects
Publ. Inst. Math. Acad. Serbe Sci
• Publ. Inst. Math. Acad. Serbe Sci
• 1957
Old and new conjectures and results about a class of Dirichlet series
• Collected Papers
• 1991
Über Dirichletreihen mit Funktionalgleichung
• Publ. Inst. Math. Acad. Serbe Sci
• 1957
Old and New Conjectures and Results about a Class of Dirichlet Series, Collected Papers, vol
• 1991