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Maass cusp form

Web4 feb. 2024 · Expression of the root number for Maass forms Take a holomorphic cusp newform, say f ∈ S k ( N) n e w, for a squarefree level N. It is an eigenvalue of the Atkin-Lehner operator, and this feature allows to express its root number as $$\... nt.number-theory modular-forms automorphic-forms l-functions maass-forms Desiderius Severus … WebMaass cusp forms are very similar to holomorphic cusp forms of weight $k \geq 2$: they have a basis of Hecke eigenforms to which one can associate $L$-functions that are …

GL(3) L-functions - IV - Annals of Mathematics

Web5 dec. 2016 · Maass cusp form symmetric power L -function AMSC: 11F30, 11F11, 11F66 Figures References Vol. 13, No. 05 Metrics History Received 1 March 2016 Accepted 6 June 2016 Published: 5 December 2016 Fourier coefficients Maass cusp form symmetric power L-function PDF download Web11 aug. 2008 · Let f be a Hecke–Maass cusp form of eigenvalue λ and square-free level N . Normalize the hyperbolic measure so that vol (Y 0 (N)) = 1 and the form f such that … tibetan traditions https://pmellison.com

Subconvexity bound for $\mathrm{GL(3)} \times \mathrm{GL(2)}

Web18 feb. 2024 · We prove an explicit formula for the Petersson norms of some normalized generic cuspidal newforms on ${\rm GSp}_4$ whose archimedean components belong … Web18 feb. 2024 · We prove an explicit formula for the Petersson norms of some normalized generic cuspidal newforms on ${\rm GSp}_4$ whose archimedean components belong to either discrete series representations or... Web5 dec. 2016 · Let ϕ be a Hecke–Maass cusp form, and a ϕ ( n) be its n th Fourier coefficient at the cusp infinity. In this paper, we are interested in the estimation on sums. ∑ n ≤ x a … thelemonadeway

Subconvexity bound for $\mathrm{GL(3)} \times \mathrm{GL(2)}

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Maass cusp form

Non-vanishing of Maass form symmetric square L-functions

WebLoosely speaking, a weight kmodular form on Γ is a holomorphic function fon H which satisfies (1.2) f(γz) = (cz+d)kf(z) for all γ∈ Γ, which in addition is holomorphic “at the cusps”. A weakly holomorphic modular form satisfies this definition but is permitted to have poles at cusps. Web3 ian. 2024 · Let $ϕ$ and $ϕ'$ be two $\textrm{GL}(3)$ Hecke--Maass cusp forms. In this paper, we prove that $ϕ=ϕ'\textrm{ or }\widetilde{ϕ'}$ if there exists a nonzero constant $κ$ such...

Maass cusp form

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Web1 apr. 2024 · Let f be a primitive Maass cusp form for a congruence subgroup Γ 0 (D) ⊂ SL (2, Z) and λ f (n) its n-th Fourier coefficient. In this paper it is shown that with knowledge … http://maasfund.org/

WebIt is shown that, under certain standard assumptions, such as extended Riemann hypotheses, the scattering matrix ϕ ( s) for generic Γ ≤ SL (2, R) is unexpectedly of order …

Web6 mar. 2007 · Maass–Poincaré Series F ( m, 2 − k, N; z ). Although the series F (m, 2 − k, N; z) are less well known, they have appeared in earlier works ( 9, 15, 16, 18, 19 ). To … Webto a weight of 1=2 harmonic Maass forms with algebraic coefficients, whose non-holomorphic parts are period integrals of a weight of 3/2 unary theta series. Essentially, these congruences are obtained from the annihilation of a cusp form g(z), related to f(z), by the Hecke operators, T(p2). The cusp form, g(z), is determined by a result of ...

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http://www.prime.sdu.edu.cn/__local/9/12/86/30D5DD4255019D9F2A3C2E81CF2_D041F189_40BA3.pdf tibetan tradition song switzerlandWebMaass cusp form for any level and character. This is accomplished by pro-ducing a bound on the difference between the ∆-eigenvalue of an authentic Maass cusp form and a … the lemonade stand teacher blogWebReceived 31 March 2011, accepted in nal form 1 July 2011, published online 20 March 2012. 2010 Mathematics Subject Classi cation 11F55, 11F72, 11M41, 35P20 (primary). Keywords: Maass form, restriction norm, automorphic form, GL 3. This material is based upon work supported by the National Science Foundation under agreement nos. DMS- tibetan tree of lifeWebMaass cusp form corresponding to the eigenvalue 2 < 1/4. Then for y in F = SL(2, 7/),f(~z) is also a Maass cusp form for the same eigenvalue, so F acts in this finite dimensional space. The principal congruence subgroup F(q) acts trivially giving a representation rc of the factor group G =F/F(q), (isomorphic to ... the lemonader by saltonWebWhen \chi χ is the trivial character, \varepsilon=\pm 1 ε =±1, and in general it is a root of unity. In the plot below, each dot corresponds to a primitive L L -function of an embedded … the lemonader instruction manualWebclassical Maass cusp forms [8]. It is known that ϑ ≤ 7/64. Currently the best known unconditional result for classical Maass cusp form coefficients is ≪ε x1027/2827+ε, which is due to Lu¨ [20]. It is a folklore conjecture that the correctupper bound is ≪ε x1/4+ε, for both holomorphiccusp forms and classical Maass cusp forms. tibetan treasures junction city caWebFaculty & Emeriti Institute for Advanced Study the lemonade stand statesville nc