Abstract
There has been much progress in recent years on some classical questions in analytic number theory. This has been due in large part to the fusion of harmonic analysis on GL(2,R) with the techniques of analytic number theory, a method inspired by A. Selberg [17]. A lot of impetus has been gained by the trace formula of Kuznetsov [11], [12], which relates Kloosterman sums with eigenfunctions of the Laplacian on GL(2,R) modulo a discrete subgroup. We cite some of the most striking applications.
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The author gratefully acknowledges the generous support of the Vaughn Foundation
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Goldfeld, D. (1987). Analytic Number Theory on GL(r,R). In: Adolphson, A.C., Conrey, J.B., Ghosh, A., Yager, R.I. (eds) Analytic Number Theory and Diophantine Problems. Progress in Mathematics, vol 70. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4816-3_9
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DOI: https://doi.org/10.1007/978-1-4612-4816-3_9
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