@inbook{92300f66befd4065b1a32446d6063fa2,

title = "On Linnik and Selberg{\textquoteright}s conjecture about sums of Kloosterman sums",

abstract = "We examine the Linnik and Selberg Conjectures concerning sums of Kloosterman sums, in all its aspects (x, m and n). We correct the precise form of the Conjecture and establish an analogue of Kuznetzov{\textquoteright}s 1/6 exponent in the mn aspect. This, perhaps somewhat surprisingly, is connected with the transional ranges associated with asymptotics of Bessel Functions of large order.",

keywords = "Kloosterman sums, Kuznetzov formula, Ramanujan-Selberg conjectures",

author = "Peter Sarnak and Jacob Tsimerman",

note = "Funding Information: 1The first author was partially supported by NSF grant DMS-0758299.",

year = "2009",

doi = "10.1007/978-0-8176-4747-6_20",

language = "English (US)",

series = "Progress in Mathematics",

publisher = "Springer Basel",

pages = "619--635",

booktitle = "Progress in Mathematics",

}