Journal of the Ramanujan Mathematical Society

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Modular forms and L-Functions with a Partial Euler Product


Affiliations
1 American Institute of Mathematics, United States
2 Bucknell University, United States
3 Chalmers University of Technology, Sweden
     

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Newforms on Γ0(N) give rise to Dirichlet series with a particular functional equation and Euler product. We directly investigate, by a numerical calculation, whether Dirichlet series with an appropriate functional equation and Euler product necessarily arise from a newform. Our calculations give new information about the role of the Euler product in the relationship between L-functions and modular forms.
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  • Modular forms and L-Functions with a Partial Euler Product

Abstract Views: 212  |  PDF Views: 0

Authors

David W. Farmer
American Institute of Mathematics, United States
Sally Koutsoliotas
Bucknell University, United States
Stefan Lemurell
Chalmers University of Technology, Sweden

Abstract


Newforms on Γ0(N) give rise to Dirichlet series with a particular functional equation and Euler product. We directly investigate, by a numerical calculation, whether Dirichlet series with an appropriate functional equation and Euler product necessarily arise from a newform. Our calculations give new information about the role of the Euler product in the relationship between L-functions and modular forms.