A dominated convergence theorem for Eisenstein series
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AbstractBased on the new approach to modular forms presented in [6] that uses rational functions, we prove a dominated convergence theorem for certain modular forms in the Eisenstein space. It states that certain rearrangements of the Fourier series will converge very fast near the cusp $$\tau = 0$$ τ = 0 . As an application, we consider L-functions associated to products of Eisenstein series and present natural generalized Dirichlet series representations that converge in an expanded half plane.
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1971 ◽
Vol 3
(1)
◽
pp. 107-108
2021 ◽
Vol 2
(2)
◽
pp. 38-49
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