Results 11 to 20 of about 317 (29)

Twist‐minimal trace formulas and the Selberg eigenvalue conjecture

Journal of the London Mathematical Society, Volume 102, Issue 3, Page 1067-1134, December 2020., 2020
Abstract 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 theorems. First, conditional on Artin's conjecture, we classify the even 2‐dimensional Artin representations of small conductor; in particular, we show that the ...
Andrew R. Booker, Min Lee, Andreas Strömbergsson   +2 more
wiley   +1 more source

Twisted Eisenstein series, cotangent‐zeta sums, and quantum modular forms

Transactions of the London Mathematical Society, Volume 7, Issue 1, Page 33-48, December 2020., 2020
Abstract We define twisted Eisenstein series Es±(h,k;τ) for s∈C, and show how their associated period functions, initially defined on the upper half complex plane H, have analytic continuation to all of C′:=C∖R⩽0. We also use this result, as well as properties of various zeta functions, to show that certain cotangent‐zeta sums behave like quantum ...
Amanda Folsom
wiley   +1 more source

p‐adic L‐functions on metaplectic groups

Journal of the London Mathematical Society, Volume 102, Issue 1, Page 229-256, August 2020., 2020
Abstract With respect to the analytic‐algebraic dichotomy, the theory of Siegel modular forms of half‐integral weight is lopsided; the analytic theory is strong, whereas the algebraic lags behind. In this paper, we capitalise on this to establish the fundamental object needed for the analytic side of the Iwasawa main conjecture — the p‐adic L‐function ...
Salvatore Mercuri
wiley   +1 more source

Selberg′s trace formula on the k‐regular tree and applications

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 8, Page 501-526, 2003., 2003
We survey graph theoretic analogues of the Selberg trace and pretrace formulas along with some applications. This paper includes a review of the basic geometry of a k‐regular tree Ξ (symmetry group, geodesics, horocycles, and the analogue of the Laplace operator). A detailed discussion of the spherical functions is given.
Audrey Terras, Dorothy Wallace
wiley   +1 more source

On the local $L^2$ -Bound of the Eisenstein series

Forum of Mathematics, Sigma
We study the growth of the local $L^2$ -norms of the unitary Eisenstein series for reductive groups over number fields, in terms of their parameters. We derive a poly-logarithmic bound on an average, for a large class of reductive groups.
Subhajit Jana, Amitay Kamber
doaj   +1 more source

$L^p$-Spectral theory of locally symmetric spaces with $Q$-rank one

, 2007
We study the $L^p$-spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces $M=\Gamma\backslash X$ with finite volume and arithmetic fundamental group $\Gamma$ whose universal covering $X$ is a symmetric space of non-compact
A. Borel, A. Borel, A. Borel, Andreas Weber, E. Brian Davies, E. Brian Davies, E. Leuzinger, G.A. Margulis, H. Garland, K. Corlette, K.-T. Sturm, L. Ji, M.E. Taylor, N.Th. Varopoulos, P. Petersen, P.B. Eberlein, R. Hempel, R. Hempel, R.J. Zimmer, R.P. Langlands, T. Hattori, V.A. Liskevich, W. Müller   +22 more
core   +2 more sources

A generalized $\mathrm{PGL}(2)$ Petersson/Bruggeman-Kuznetsov formula for analytic applications

Forum of Mathematics, Sigma
We develop generalized Petersson/Bruggeman-Kuznetsov (PBK) formulas for specified local components at non-archimedean places. In fact, we introduce two hypotheses on non-archimedean test function pairs $f \leftrightarrow \pi (f)$ , called geometric
Yueke Hu, Ian Petrow, Matthew P. Young
doaj   +1 more source

Theta functions, fourth moments of eigenforms and the sup-norm problem II

Forum of Mathematics, Pi
Let f be an $L^2$ -normalized holomorphic newform of weight k on $\Gamma _0(N) \backslash \mathbb {H}$ with N squarefree or, more generally, on any hyperbolic surface $\Gamma \backslash \mathbb {H}$ attached to an Eichler order of ...
Ilya Khayutin, Paul D. Nelson, Raphael S. Steiner   +2 more
doaj   +1 more source

Quantum Limits of Eisenstein Series and Scattering states

, 2013
We identify the quantum limits of scattering states for the modular surface. This is obtained through the study of quantum measures of non-holomorphic Eisenstein series away from the critical line.
Colin de Verdiére, Gradshteyn, Holowinsky, Iwaniec, Iwaniec, Jakobson, Koyama, Lindenstrauss, Luo, Meurman, Michel, Morten S. Risager, Nicole Raulf, Petridis, Selberg, Shnirelman, Soundararajan, Titchmarsh, Truelsen, Yiannis N. Petridis, Zelditch, Zelditch   +21 more
core   +1 more source

Decomposition of splitting invariants in split real groups

, 2010
To a maximal torus in a quasi-split semi-simple simply-connected group over a local field of characteristic 0, Langlands and Shelstad construct a cohomological invariant called the splitting invariant, which is an important component of their endoscopic ...
Agaoka, Demazure, Langlands, Langlands, Langlands, Shelstad, Shelstad, Shelstad, Shelstad, Shelstad, Shelstad, Shelstad, Shelstad, Springer, Tasho Kaletha   +14 more
core   +1 more source