We describe a new method for constraining Laplacian spectra of hyperbolic surfaces and 2-
orbifolds. The main ingredient is consistency of the spectral decomposition of integrals of …

We constrain the low-energy spectra of Laplace operators on closed hyperbolic manifolds
and orbifolds in three dimensions, including the standard Laplace-Beltrami operator on …

We study theoretical and practical aspects of high-precision computation of Maass forms.
First, we compute to over 1000 decimal places the Laplacian and Hecke eigenvalues for the …

We present a group-theoretic criterion under which one may verify the Artin conjecture for
some (nonmonomial) Galois representations, up to finite height in the complex plane. In …

We exhibit the first examples of hyperbolic three-manifolds for which the Seiberg-Witten
equations do not admit any irreducible solution. Our approach relies on hyperbolic geometry …

AMS :: Bulletin of the American Mathematical Society Skip to Main Content American
Mathematical Society American Mathematical Society MathSciNet Bookstore Publications …

We estimate the sums∑ c≤ x S (m, n, c, χ) c, where the are Kloosterman sums associated
with a multiplier system of half-integral weight on the modular group. Our estimates are …

Building on work of Hardy and Ramanujan, Rademacher proved a well-known formula for
the values of the ordinary partition function p (n). More recently, Bruinier and Ono obtained …

On compact Riemann surfaces, the Laplacian has a discrete, non-negative spectrum of
eigenvalues of finite multiplicity. The spectrum is intrinsically linked to the geometry of the …

We derive a fully explicit version of the Selberg trace formula for twist‐minimal Maass forms
of weight 0 and arbitrary conductor and nebentypus character, and apply it to prove two …