Remarks on modular symbols for Maass wave forms

Manin, Yuri I.

doi:10.2140/ant.2010.4.1091

Cited by 6 publications

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“…As kernels, they produce products of L-functions for Maass cusp forms; see Theorem 2.9. The main motivation for this construction was its potential use in the rapidly developing study of periods of Maass forms [Bruggeman et al 2013;Lewis and Zagier 2001;Manin 2010;Mühlenbruch 2006]. In developing the properties of (1-7), we require a certain kernel (z; s, s ) as defined in (9-1).…”

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confidence: 99%

Kernels for products ofL-functions

Diamantis

O’Sullivan

2013

Algebra Number Theory

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confidence: 99%

Kernels for products ofL-functions

Diamantis

O’Sullivan

2013

Algebra Number Theory

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“…The formalism of pseudomeasures was also used in [33] to describe modular symbols for Maass wave forms, based on the work of Lewis-Zagier [26]. In particular, Manin gives in [33] an interpretation of the Lévy-Mellin transform of [35] as an analog at arithmetic infinity (at the archimedan prime) of the p-adic Mellin-Mazur transform. 4.2.…”

Section: Consider a Complex Valued Function F Which Is Defined On Pairsmentioning

confidence: 99%

Noncommutative Geometry and Arithmetic

Marcolli

2011

Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)

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Abstract. This is an overview of recent results aimed at developing a geometry of noncommutative tori with real multiplication, with the purpose of providing a parallel, for real quadratic fields, of the classical theory of elliptic curves with complex multiplication for imaginary quadratic fields. This talk concentrates on two main aspects: the relation of Stark numbers to the geometry of noncommutative tori with real multiplication, and the shadows of modular forms on the noncommutative boundary of modular curves, that is, the moduli space of noncommutative tori.

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“…Some period functions were attached bijectively to Maass cusp forms according to the spectral parameter s and its cohomological counterpart was described (see [18,2]). Similar modification to Hecke operators on the period space has also been applied to that of Maass cusp forms with spectral parameter s [21,22,20].…”

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confidence: 99%

Periods of Jacobi forms and the Hecke operator

Choie

Jin

2013

Journal of Mathematical Analysis and Applications

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A Hecke action on the space of periods of cusp forms, which is compatible with that on the space of cusp forms, was first computed using continued fraction [19] and an explicit algebraic formula of Hecke operators acting on the space of period functions of modular forms was derived by studying the rational period functions [8]. As an application an elementary proof of the Eichler-Selberg trace formula was derived [26]. Similar modification has been applied to period space of Maass cusp forms with spectral parameter s [21,22,20]. In this paper we study the space of period functions of Jacobi forms by means of Jacobi integral and give an explicit description of Hecke operator acting on this space. a Jacobi Eisenstein series E 2,1 (τ, z) of weight 2 and index 1 is discussed as an example. Periods of Jacobi integrals are already appeared as a disguised form in the work of Zwegers to study Mordell integral coming from Lerch sums [27] and mock Jacobi forms are typical example of Jacobi integral [9].

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Remarks on modular symbols for Maass wave forms

Cited by 6 publications

References 20 publications

Kernels for products ofL-functions

Kernels for products ofL-functions

Noncommutative Geometry and Arithmetic

Periods of Jacobi forms and the Hecke operator

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