Results 1 to 10 of about 307 (28)
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 +2 more
doaj +1 more source
CM-points and Lattice counting on arithmetic compact Riemann surfaces [PDF]
, 2020 Let $X(D,1) =\Gamma(D,1) \backslash \mathbb{H}$ denote the Shimura curve of level $N=1$ arising from an indefinite quaternion algebra of fixed discriminant $D$. We study the discrete average of the error term in the hyperbolic circle problem over Heegner
Alsina, Montserrat, Chatzakos, Dimitrios
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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 +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
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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
Arithmetic expressions of Selberg's zeta functions for congruence subgroups [PDF]
, 2006 In Sarnak's paper, it was proved that the Selberg zeta function for SL(2,Z) is expressed in terms of the fundamental units and the class numbers of the primitive indefinite binary quadratic forms.
Hashimoto, Yasufumi
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Analytic Continuation of Resolvent Kernels on noncompact Symmetric Spaces [PDF]
, 2003 Let X=G/K be a symmetric space of noncompact type and let L be the Laplacian associated with a G-invariant metric on X. We show that the resolvent kernel of L admits a holomorphic extension to a Riemann surface depending on the rank of the symmetric ...
80 +10 more
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Artin formalism for Selberg zeta functions of co-finite Kleinian groups [PDF]
, 2008 Let $\Gamma\backslash\mathbb H^3$ be a finite-volume quotient of the upper-half space, where $\Gamma\subset {\rm SL}(2,\mathbb C)$ is a discrete subgroup.
Brenner, Eliot, Spinu, Florin
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Maass cusp forms for large eigenvalues [PDF]
, 2003 We investigate the numerical computation of Maass cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed r=40000.
Then, H.
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