Functional Equations of Dirichlet Series Derived from Non-Analytic Automorphic Forms of a Certain Type
Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 87-94
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Let f(τ) be a complex valued function, defined and analytic in the upper half of the complex τ plane (τ = x+iy, y > 0), such that f(τ + λ)= f(τ) where λ is a positive real number and f(—1/τ) = γ(—iτ)kf(τ), k being a complex number. The function (—iτ)k is defined as exp(k log(—iτ) where log(—iτ) has the real value when —iτ is positive. Every such function is said to have signature (λ, k, γ) in the sense of E. Hecke [1] and has a Fourier expansion of the type f(τ) = a0 + σ an exp(2πin/λ), (n = 1,2,...), if we further assume that f(τ) = O(|y|-c) as y tends to zero uniformly for all x, c being a positive number.
Rao, V. Venugopal. Functional Equations of Dirichlet Series Derived from Non-Analytic Automorphic Forms of a Certain Type. Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 87-94. doi: 10.4153/CMB-1975-016-9
@article{10_4153_CMB_1975_016_9,
author = {Rao, V. Venugopal},
title = {Functional {Equations} of {Dirichlet} {Series} {Derived} from {Non-Analytic} {Automorphic} {Forms} of a {Certain} {Type}},
journal = {Canadian mathematical bulletin},
pages = {87--94},
year = {1975},
volume = {18},
number = {1},
doi = {10.4153/CMB-1975-016-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-016-9/}
}
TY - JOUR AU - Rao, V. Venugopal TI - Functional Equations of Dirichlet Series Derived from Non-Analytic Automorphic Forms of a Certain Type JO - Canadian mathematical bulletin PY - 1975 SP - 87 EP - 94 VL - 18 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-016-9/ DO - 10.4153/CMB-1975-016-9 ID - 10_4153_CMB_1975_016_9 ER -
%0 Journal Article %A Rao, V. Venugopal %T Functional Equations of Dirichlet Series Derived from Non-Analytic Automorphic Forms of a Certain Type %J Canadian mathematical bulletin %D 1975 %P 87-94 %V 18 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-016-9/ %R 10.4153/CMB-1975-016-9 %F 10_4153_CMB_1975_016_9
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