Abstract
This was later extended by Deshouillers and Iwaniec [9] and their work was then used by Bombieri et al. [2, 3] to prove some spectacular results in number theory. In an unpublished note Zagier gave a new proof of the Kuznietsov trace formula (cf. Iwaniec [13]). His method can be generalized to the GL(n) case as pointed out by Friedberg [10] and was later carried out by Joyner [18] in order to extend the Kuznietsov trace formula to real quadratic number fields. The generalization to the group GL(n) was also done by Goldfeld [11] from which he expressed the principal cuspidal contribution to the Selberg trace formula in terms of special values of quadratic L-functions. An adelic version of the Kuznietsov trace formula was formulated by the author in [24] and by Jacquet and Rallis [14]. Comparing the Kuznietsov
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