This function, when k = 2, was introduced by Y. Motohashi [15] (see also [16]), and its properties were further studied in [10] and [11]. The latter work also contains some results on the functionâ€¦ (More)

with s = Ïƒ + it denote the Mellin transform of f(x). Mellin transforms play a fundamental rÃ´le in Analytic Number Theory. They can be viewed, by a change of variable, as special cases of Fourierâ€¦ (More)

Most of arithmetically significant Dirichlet series such as the Riemann zeta-function Î¶(s), Dirichlet L-functions, and Hecke L-functions associated with various cusp forms satisfy Riemannianâ€¦ (More)

We prove, in standard notation from spectral theory, the asymptotic formula (B > 0) âˆ‘ Îºjâ‰¤T Î±jHj( 1 2 ) = ( T Ï€ ) 2 âˆ’ BT log T +O(T (log T )), by using an approximate functional equation for Hj( 1 2 )â€¦ (More)

We prove, in standard notation from spectral theory, the asymptotic formula (B > 0) âˆ‘ Îºjâ‰¤T Î±jHj( 1 2 ) = ( T Ï€ ) 2 âˆ’ BT log T +O(T (log T )), by using an approximate functional equation for Hj( 1 2 )â€¦ (More)