Maass converse theorems

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August undefined, 2024

Websimilar relations for Maass forms of integral and half-integral weight, and give converse theorems for automorphic distributions and Maass forms of level N. As an application of our converse theorems, we construct Maass forms from the two-variable zeta functions related to quadratic forms studied by Peter [29] and the fourth author [46]. WebWeil’s converse theorem for Maass forms and cancellation of zeros Michael Neururer, Thomas D Oliver Mathematics Acta Arithmetica 2024 We first prove a new converse theorem for Dirichlet series of Maass type which does not assume an Euler product. The underlying idea is a geometric generalisation of Weil's classical argument. By… 10 PDF

Converse theorems for automorphic distributions and …

Web1 mai 2024 · In Section 4, we study the Koecher-Maass series associated to Hermitian modular forms of degree 2, level N, twisted by automorphic functions on H 3. In Section 5, we recall a converse theorem of Hermitian cusp forms. With these preparations, we complete the proof of Theorem 1 in Section 6. WebA Converse Theorem and the Saito-Kurokawa Lift 353 Proof. The functional equation in the case kD0 is found by computing the scattering matrix in [Iw;Theorem 6.5]. The functional equation for general even k<0 is deduced from this by successively applying the Maass operator LkD¡iy@xCy@y¡k=2;since L¡kE ¡kD(sCk=2)E¡k¡2. seehafer news manitowoc wi

Automorphic pairs of distributions on R, and Maass forms of real ...

Web2 feb. 2024 · We first prove a new converse theorem for Dirichlet series of Maass type which does not assume an Euler product. The underlying idea is a geometric … WebA. Booker, M. Krishnamurthy. Published 2014. Mathematics. International Mathematics Research Notices. We prove a generalization of the classical converse theorem of Weil, … WebL-FUNCTIONS, CONVERSE THEOREMS, AND FUNCTORIALITY* F. Shahidi** x1.Background and Functoriality. f= holomorphic modular cusp form or a Maass form with respect to Γ 0(N) = eigenfunction for all the Hecke operator as well as Laplacian = −y2 @ 2 @x2 @y2 if k=0; where kis the weight of f: a n= Fourier coe cient of f; a 1 =1 a p= p k−1 2 seehafer news for the record

$Abstract. arXiv:2101.03101v1 [math.NT] 8 Jan 2024$

Andrew Booker

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 of weight = 0 under this weaker assumptions is obtained in Neururer and Oliver [23], which appeared very recently in the final stage of … seehafer cottbusWebA 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... seehealth123

"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 … " - Maass converse theorems

Maass converse theorems

L-FUNCTIONS, CONVERSE THEOREMS, F. Shahidi** - Institute for …

Web19 sept. 2015 · The theorem of Blasius, Clozel and Ramakrishnan that the eigenvalues of Hecke operators for Maass forms of Galois type are algebraic numbers, which the author had discussed in the original paper, has to be considered unproved up to now.

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WebL-FUNCTIONS, CONVERSE THEOREMS, AND FUNCTORIALITY* F. Shahidi** x1. Background and Functoriality. f= holomorphic modular cusp form or a Maass form with … Webof our converse theorems, we construct Maass forms from the two-variable zeta functions related to quadratic forms studied by Peter [29] and the fourth author …

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 … Web20 aug. 2024 · A basic limitation of the Maass converse theorem is that it provides automorphy only with respect to a discrete subgroup generated by translations and one inversion. For the case of n>1, it seems difficult to determine the generators of \Gamma _S.

Web18 sept. 2024 · Two converse theorems for Maass forms September 2024 Authors: Michael Neururer Thomas Oliver Teesside University Preprints and early-stage research … WebWeil's converse theorem for Maass forms and cancellation of zeros Abstract: We prove two principal results. Firstly, we characterise Maass forms in terms of functional …

WebFirstly, 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 ...

WebWe 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 … seehafer templinWebm,p(d;X,t) for all prime numbers p (cf. Theorems 4.3.1, 4.3.2, and 4.3.6). In Section 5, by using explicit formulas for Pˆ m,p(d;X,t), we immediately get an explicit formula of L(s,Im(f)). Using the same argument as in the proof our main result, we can give an explicit formula of the Koecher-Maass series of the Hermitian Eisenstein series of ... seehd freeWebA converse theorem in the theory of automorphic forms refers to the equivalence of Dirichlet series satisfying certain analytic properties, on the one hand, and automorphic forms over some group, on the other. ... Other results of this kind are Maass’ converse theorem for Maass waveforms of level 1 , its generalization to ... seehas fahrplanWebOther 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 ... seehalde romanshornWeb8 ian. 2024 · We further consider Dirichlet series attached to a harmonic Maass formof polynomial growth, study its analytic properties, and prove an analogue ofWeil's … seehamer campingWeb13 dec. 2024 · Our goal is converse theorems for automorphic distributions and Maass forms of level N characterizing them by analytic properties of the associated L -functions. … seehd streamWeb1 mai 2014 · We show how this new interpretation naturally leads to strengthenings of the theorems of Bruinier, Ono and Rhoades, by answering in the affirmative conjectures about the field of definitions of Fourier coefficients of harmonic weak Maass forms. ... An analogue of Weil’s converse theorem for harmonic Maass forms of polynomial growth. 25 May ... seehan littlefeather