Maass converse theorems
Web1 dec. 2016 · An adaptation of Maass's converse theorem. In , Maass proved a converse theorem for non-holomorphic modular forms of weight zero which are eigenfunctions of 0. In he generalized this result to non-holomorphic modular forms of complex weight (α, β), with r = α − β real, which are solutions of a certain differential equation. WebA converse theorem for Maass forms on the full modular group was proved by Raghunathan [23]. The Riemann hypothesis for L-functions of Maass wave forms for PSL (2, Z) was tested numerically...
Maass converse theorems
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WebMost familiar is the converse theorem due to Hecke , which establishes an equivalence between modular forms on S L 2 (Z) and Dirichlet series satisfying a certain functional … Web23 ian. 2024 · I found that one may need converse theorem for Rankin-Selberg $L$-functions, which seems intractable. I also tried to directly construct the candidate …
Web18 sept. 2024 · Two converse theorems for Maass forms September 2024 Authors: Michael Neururer Thomas Oliver Teesside University Preprints and early-stage research … Weblevel 1 [15], its generalization to Γ0(N) by Neururer and Oliver [20], converse theorems for Jacobi forms [14, 16, 17], and Maass Jacobi forms [10]. The converse theorem for GLn is a great achievement of several authors through a string of papers [5, 12, 13]. 1.1. Statement of the main result. In order to state our converse theorem for the ...
WebL-FUNCTIONS, CONVERSE THEOREMS, AND FUNCTORIALITY* F. Shahidi** x1. Background and Functoriality. f= holomorphic modular cusp form or a Maass form with … WebOther results of this kind are Maass’ converse theorem for Maass waveforms of level 1 [15], its generalization to Γ0(N) by Neururer and Oliver [20], converse theorems for Jacobi forms [16, 17], Siegel modular forms [14], and Maass Jacobi forms [10]. The con-verse theorem for GLn is a great achievement of several authors through a string of ...
Web2 feb. 2024 · A Weil-type converse theorem for the Dirichlet series of Maass forms was stated in [2], though there is an apparently undocumented error in the statement of the non-holomorphic analogue of...
Webconverse theorem for automorphic representations of GL2(AF) over global fields F [JL70]. In particular, the Jacquet–Langlands converse theorem applies to holomorphic … new visions rcfWebA. Booker, M. Krishnamurthy. Published 2014. Mathematics. International Mathematics Research Notices. We prove a generalization of the classical converse theorem of Weil, … mi homes farmingtonWeb1258 R. Raghunathan / Journal of Number Theory 130 (2010) 1255–1273 Theorem 2.1. Let D(s) be a Dirichlet series satisfying the conditions D1, D2and D3for ν ∈/ Z,andlet f(z) be the function associated to the series D (s)as above.Then f z) is a Maass form for SL2 Z with eigenvalue ν(1−ν). Corollary 2.2. The possible poles of L(s) can be described as follows. … mi homes free poolWeb18 sept. 2024 · Two converse theorems for Maass forms September 2024 Authors: Michael Neururer Thomas Oliver Teesside University Preprints and early-stage research may not have been peer reviewed yet. Abstract... new vision storeWebWe will now state our converse theorem in the special case of weakly holomorphic cusp forms for SL 2(Z). The general statement for all harmonic Maass forms of all levels (Theo-rem5.1) and its proof will be given in §5. Theorem 1.1. Let (a(n)) n n 0 be a sequence of complex numbers such that a(n) = O(eC p n) as n!1, for some C>0:For each z2H ... mi homes green oak crossingWebFirstly, we characterise Maass forms in terms of functional equations for Dirichlet series twisted by primitive characters. The key point is that the twists are allowed to be meromorphic. This weakened analytic assumption applies in the context of our second theorem, which shows that the quotient of the symmetric square L-function of a Maass ... mi homes georgetown txWebWe further consider Dirichlet series attached to a harmonic Maass form of polynomial growth, study its analytic properties, and prove an analogue of Weil's converse … mi homes founders park