Direct proof of energy conservation for automorphic wave equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 2, pp. 247-249
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The resonances in the problem of scattering on the fundamental domain of the modular group are related to the zeros of Riemann's $\zeta$ function on the critical line [1]. Therefore, the rate of decrease of the energy in the solution given by the Eisenstein series on the translationally invariant subspace is determined by the position of the zeros of the $\zeta$ function. Decrease of the energy can be expected only if there is mutual compensation of the terms of the series [2]. The question of corresponding compensations in the simpler situation in the complete space is therefore of interest.
@article{TMF_1993_97_2_a6,
author = {A. M. Khodakovskii},
title = {Direct proof of energy conservation for automorphic wave equation},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {247--249},
publisher = {mathdoc},
volume = {97},
number = {2},
year = {1993},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1993_97_2_a6/}
}
A. M. Khodakovskii. Direct proof of energy conservation for automorphic wave equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 2, pp. 247-249. http://geodesic.mathdoc.fr/item/TMF_1993_97_2_a6/