Search
Search Results
-
The functional equations of Langlands Eisenstein series for SL(n, ℤ)
In this paper, we present a very simple explicit description of Langlands Eisenstein series for SL( n , ℤ). The functional equations of these...
-
Isolation of the cuspidal spectrum: The function field case
Isolating cuspidal automorphic representations from the whole automorphic spectrum is a basic problem in the trace formula approach. For example,...
-
The second moment of GL(3) × GL(2) L-functions at special points from GL(3) forms
For a fixed even SL(2, ℤ) Hecke-Maass form f , we get an estimate for the second moment of L ( s , φ j × f ) at special points, where φ j runs over an...
-
A Prime Geodesic Theorem of Gallagher Type for Riemann Surfaces
We consider a cofinite Fuchsian group of the first kind with finitely many inequivalent parabolic elements and a unitary multiplier system of an...
-
Analytic Torsion and Dynamical Flow:A Survey on the Fried Conjecture
Given an acyclic and unitarily flat vector bundle on a closed manifold, Fried conjectured an equality between the analytic torsion and the value at...
-
Transmission Eigenvalues and the Riemann Zeta Function in Scattering Theory for Automorphic Forms on Fuchsian Groups of Type I
We introduce the concept of transmission eigenvalues in scattering theory for automorphic forms on fundamental domains generated by discrete groups...
-
Stable local trace formula
Langlands program is the central concern of modern number theory. In general, we think that the main tool for studying this program is the trace...
-
On elliptic factors in real endoscopic transfer I
This paper is concerned with the structure of packets of representations and some refinements that are helpful in endoscopic transfer for real...
-
On the remainder term in the Weyl law for cofinite Kleinian groups with finite dimensional unitary representation
We obtain a new bound for the remainder term in the Weyl law for general cofinite Kleinian groups with finite dimensional unitary representation by...
-
Harmonic analysis on the Iwahori–Hecke algebra
These are purely expository notes of Opdam’s analysis [O1] of the trace form τ ( f ) = f ( e ) on the Hecke algebra H = C c ( I \ G / I ) of compactly supported...
-
Trace formulae and applications to class numbers
In this paper we compute the trace formula for Hecke operators acting on automorphic forms on the hyperbolic 3-space for the group PSL 2 (
... -
On the Critical Line of Convex Co-Compact Hyperbolic Surfaces
Let Γ be a convex co-compact Fuchsian group. We formulate a conjecture on the critical line, i.e. what is the largest half-plane with finitely many...
-
The Trace Formula for the Heat Semigroup with Polynomial Potential
We consider the heat semigroup $$e^{-\frac{t}{\hbar}H}, t > 0,\,\, {\rm...
-
Large Values of Eigenfunctions on Arithmetic Hyperbolic 3-Manifolds
We prove that, on a distinguished class of arithmetic hyperbolic 3-manifolds, there is a sequence of L 2 -normalized high-energy Hecke–Maass...
-
Holomorphic torsion and closed geodesics
Extending the rank-one case by David Fried, the holomorphic torsion of a compact locally symmetric manifold is expressed as a special value of a zeta...