Journal of the Ramanujan Mathematical Society

David W. Farmer ¹, Sally Koutsoliotas ², Stefan Lemurell ³

Affiliations
1 American Institute of Mathematics, US
2 Bucknell University, US
3 Chalmers University of Technology, SE

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.

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