Symmetric and locally symmetric spaces arise in different contexts. Many natural spaces of
this type are not compact and, for many applications, it is necessary to compactify them. This …

Strong bounds—going beyond Sarnak's density hypothesis—are obtained for the number of
automorphic forms for the group Γ 0 (q)⊆ SL (n, Z) violating the Ramanujan conjecture at …

Strong bounds are obtained for the number of automorphic forms for the group Γ 0 (q)⊆ Sp
(4, Z) Γ_0(q)⊆Sp(4,Z) violating the Ramanujan conjecture at any given unramified place …

The authors prove a general form of the sum formula $\mathrm {SL} _2 $ over a totally real
number field. This formula relates sums of Kloosterman sums to products of Fourier …

In one guise or another, many mathematicians are familiar with certain arithmetic groups,
such as $\mathbf {Z} $ or $\textrm {SL}(n,\mathbf {Z}) $. Yet, many applications of arithmetic …

Abstract We obtain a Voronoi–Oppenheim summation formula for divisor functions of totally
real number fields. This generalizes a formula proved by Oppenheim in 1927. We use a …

Using Langlands's {\it Beyond Endoscopy} idea and analytic number theory techniques, we
study the Asai L-function associated to a real quadratic field $\mathbf {K}/\Q. $ If the Asai L …

Using Langlands's beyond endoscopy idea, we study the Asai $ L $-function associated to a
real quadratic field $\Bbb {K}/\Bbb {Q} $. We prove that the Asai $ L $-function associated to …

We construct $ p $-adic measures which interpolate the special values of reciprocals of $ p $-
adic $ L $-functions of totally real number fields $ K $ at negative integers. These measures …

This paper is a first attempt at getting information on a symmetric power lift of a GL2
automorphic representation via a trace formula that is beyond endoscopic techniques. In …