Assuming a special version of the Montgomery-Odlyzko law on the pair correlation of zeros of the Riemann zeta function conjectured by Rudnick and Sarnak and assuming the Riemann Hypothesis, we proveâ€¦ (More)

In this paper we Â®rst prove a weighted prime number theorem of an ``o Ìˆ-diagonal'' type for Rankin-Selberg L-functions of automorphic representations of GLm and GLm 0 over Q. Then for m Âˆ 1, or underâ€¦ (More)

This is a joint work with Yangbo Ye. We prove a subconvexity bound for Rankin-Selberg L-functions L(s, fâŠ—g) associated with a Maass cusp form f and a fixed cusp form g in the aspect of the Laplaceâ€¦ (More)

Abstract Let Ï€ and Ï€ be automorphic irreducible cuspidal representations of GLm( ) and GLmâ€² ( ), respectively. Assume that Ï€ and Ï€ are unitary and self contragredient. In this article we will give anâ€¦ (More)

It is conjectured that Lagrangeâ€™s theorem of four squares is true for prime variables, i.e. all positive integers n with n 4 Ã°mod 24Ãž are the sum of four squares of primes. In this paper, the sizeâ€¦ (More)

Let Ï€ be an automorphic irreducible cuspidal representation of GLm over a Galois (not necessarily cyclic) extension E of Q of degree `. Assume that Ï€ is invariant under the action of the Galois groupâ€¦ (More)

Let Ï€ and Ï€ be automorphic irreducible unitary cuspidal representations of GLm(QA) and GLmâ€²(QA), respectively. Assume that Ï€ and Ï€ â€² are self contragredient. Under the Ramanujan conjecture on Ï€ and Ï€â€¦ (More)

We prove a weighted version of Selbergâ€™s orthogonality conjecture for automorphic L-functions attached to irreducible cuspidal representations of GLm over Q. Using this weighted orthogonality, weâ€¦ (More)