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Maass converse theorems

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 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 ...

Koecher-Maass series associated to Hermitian modular

Web13 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. As an application of our... 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 … round engine https://jtcconsultants.com

ConversetheoremsforautomorphicdistributionsandMaass …

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. Web18 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... 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 … round engine round up 2021

An explicit construction of non-tempered cusp forms on

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Maass converse theorems

Two converse theorems for Maass forms Request PDF

Web18 sept. 2024 · Two converse theorems for Maass forms September 2024 Authors: Michael Neururer Thomas Oliver Teesside University Preprints and early-stage research … WebWe 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&gt;0:For each z2H ...

Maass converse theorems

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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 ...

WebarXiv:1809.06586v4 [math.NT] 17 Jul 2024 WEIL’S CONVERSE THEOREM FOR MAASS FORMS AND CANCELLATION OF ZEROS MICHAEL NEURURER AND THOMAS … 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 …

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. Booker, M. Krishnamurthy. Published 2014. Mathematics. International Mathematics Research Notices. We prove a generalization of the classical converse theorem of Weil, …

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 …

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 preparation of this... strathearn art walk 2022Webm,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 ... strathearn coat of armsWeb2 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... round engravable gold charmsWeb13 mai 2024 · As an application of our converse theorems, we construct Maass forms from the two-variable zeta functions related to quadratic forms studied by Peter and the fourth … strathearn community campusWebA 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... round england cruisesWebA converse theorem for Jacobi{Maass forms and applications Introduction to Chapter 1 The main purpose of converse theorems is to establish a one-to-one correspondence between automorphic forms over some group, on the one hand, and Dirichlet series satisfying some nice analytic properties, on the other. round engraved cutting boardsWebL-FUNCTIONS, CONVERSE THEOREMS, AND FUNCTORIALITY* F. Shahidi** x1. Background and Functoriality. f= holomorphic modular cusp form or a Maass form with … round engraving plates