The Dirichlet series of Koecher and Maaß and modular forms of weight 3/2

Böcherer, Siegfried; Schulze-Pillot, Rainer

doi:10.1007/bf02570834

Cited by 33 publications

(57 citation statements)

References 17 publications

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“…Here it will be shown that for ;O and X2 fixed and N a large prime many P:(s) achieve this lower bound. ~The paper [1] contains a different proof of this criterion which also gives the theta series representation explicitly. …”

Section: Then There Is a Positive Absolute Constant C And A Constant mentioning

confidence: 96%

The critical order of vanishing of automorphicL-functions with large level

Duke

1995

Invent Math

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Section: Then There Is a Positive Absolute Constant C And A Constant mentioning

confidence: 96%

The critical order of vanishing of automorphicL-functions with large level

Duke

1995

Invent Math

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“…However, we note that results of Gross [9] when N is prime, and Böcherer and Schulze-Pillot [2] when N is squarefree indicate that a preimage of φ E under the Shimura correspondence is a linear combination of the theta series associated to ternary forms if and only if for the L-series of φ E , L(φ E , 1) = 0. This is conjectured to be the case if and only if the rank of E is zero.…”

Section: Theorem 1 For Every Isogeny Class Of Elliptic Curves E Of Ementioning

confidence: 99%

Rational eigenvectors in spaces of ternary forms

Lehman¹

1997

Math. Comp.

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Abstract. We describe the explicit computation of linear combinations of ternary quadratic forms which are eigenvectors, with rational eigenvalues, under all Hecke operators. We use this process to construct, for each elliptic curve E of rank zero and conductor N < 2000 for which N or N/4 is squarefree, a weight 3/2 cusp form which is (potentially) a preimage of the weight two newform φ E under the Shimura correspondence.

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“…The case of Yoshida lifts of weight two has also been treated (see [3]). The author [14] and Ryan and Tornaría [16] recently argued that the conjecture should also hold in the paramodular setting, and proved that it holds for Gritsenko lifts.…”

Section: Introductionmentioning

confidence: 99%

“…The author [14] and Ryan and Tornaría [16] recently argued that the conjecture should also hold in the paramodular setting, and proved that it holds for Gritsenko lifts. For [3] Spaces of classical Siegel modular forms 395…”

Section: Introductionmentioning

confidence: 99%

Efficiently Generated Spaces of Classical Siegel Modular Forms and the Böcherer Conjecture

Raum¹

2010

J. Aust. Math. Soc.

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We state and verify up to weight 172 a conjecture on the existence of a certain generating set for spaces of classical Siegel modular forms. This conjecture is particularly useful for calculations involving Fourier expansions. Using this generating set, we verify the Böcherer conjecture for nonrational eigenforms and discriminants with class number greater than one. As a further application we verify another conjecture for weights up to 150 and investigate an analog of the Victor-Miller basis. Additionally, we describe some arithmetic properties of the basis we found.2010 Mathematics subject classification: primary 11F46; secondary 11F67, 11Y99.

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The Dirichlet series of Koecher and Maaß and modular forms of weight 3/2

Cited by 33 publications

References 17 publications

The critical order of vanishing of automorphicL-functions with large level

The critical order of vanishing of automorphicL-functions with large level

Rational eigenvectors in spaces of ternary forms

Efficiently Generated Spaces of Classical Siegel Modular Forms and the Böcherer Conjecture

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