Geodesic
Comparison of spectra
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 1, Tome 228 (1996), pp. 67-76 
A. I. Vinogradov. Comparison of spectra. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 1, Tome 228 (1996), pp. 67-76. http://geodesic.mathdoc.fr/item/ZNSL_1996_228_a6/
@article{ZNSL_1996_228_a6,
     author = {A. I. Vinogradov},
     title = {Comparison of spectra},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {67--76},
     year = {1996},
     volume = {228},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_228_a6/}
}
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The Selberg conjecture concerning the absence of small eigenvalues in the spectrum of congruence group is proved by the comparison of two different spectral expansions for one and the same arithmetic convolution averaged by a shift. Bibl. 6 titles.