Results 1 to 10 of about 39 (39)

An orthogonality relation for $\mathrm {GL}(4, \mathbb R) $ (with an appendix by Bingrong Huang)

Forum of Mathematics, Sigma, 2021
Orthogonality is a fundamental theme in representation theory and Fourier analysis. An orthogonality relation for characters of finite abelian groups (now recognized as an orthogonality relation on $\mathrm {GL}(1)$) was used by Dirichlet to prove ...
Dorian Goldfeld, Eric Stade, Michael Woodbury   +2 more
doaj   +1 more source

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

Error term of the mean value theorem for binary Egyptian fractions

Open Mathematics, 2020
In this article, the error term of the mean value theorem for binary Egyptian fractions is studied. An error term of prime number theorem type is obtained unconditionally. Under Riemann hypothesis, a power saving can be obtained.
Xiao Xuanxuan, Zhai Wenguang
doaj   +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

Strongly tempered hyperspherical Hamiltonian spaces

Forum of Mathematics, Sigma
In this paper, we give a complete list of strongly tempered anomaly-free hyperspherical Hamiltonian spaces-those that are dual to symplectic vector spaces under the relative Langlands duality.
Zhengyu Mao, Chen Wan, Lei Zhang
doaj   +1 more source

Geometric side of a local relative trace formula

, 2019
International audienceFollowing a scheme suggested by B. Feigon, we investigate a local relative trace formula in the situation of a reductive p-adic group G relative to a symmetric subgroup H " HpF q where H is split over the local field F of ...
Souaifi, Sofiane, Delorme, Patrick, Harinck, Pascale   +2 more
core   +1 more source

The global Gan-Gross-Prasad conjecture for unitary groups. II. From Eisenstein series to Bessel periods

Forum of Mathematics, Pi
We state and prove an extension of the global Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture to the case of some Eisenstein series on unitary groups $U_n\times U_{n+1}$ .
Raphaël Beuzart-Plessis, Pierre-Henri Chaudouard   +1 more
doaj   +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