Modulformen auf Γ0(N) mit rationalen Periodenmit rationalen Perioden

Antoniadis, Jannis A.

doi:10.1007/bf02567676

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Introduction3

Periods Of Cusp Forms Of Level2

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2005

2024

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Cited by 8 publications

(12 citation statements)

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“…The isomorphism is explicitly given by sending f to the class of 1 2 (π f −π f ) where π f resp.,π f are the cocycles given by…”

Section: Periods Of Cusp Forms Of Levelmentioning

confidence: 99%

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Representations of integers as sums of an even number of squares

Imamoḡlu

Kohnen

2005

Math. Ann.

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“…The isomorphism is explicitly given by sending f to the class of 1 2 (π f −π f ) where π f resp.,π f are the cocycles given by…”

Section: Periods Of Cusp Forms Of Levelmentioning

confidence: 99%

“…It suffices to show that 1 2 (π f −π f ) = 0 under our given assumptions. A cocycle is determined by its values on the generators of the group.…”

Section: Periods Of Cusp Forms Of Levelmentioning

confidence: 99%

Representations of integers as sums of an even number of squares

Imamoḡlu

Kohnen

2005

Math. Ann.

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“…(Note that periods and the Hecke operators on periods have been studied by a number of mathematicians. To name a few, see [1,5,8,12,14,15,17,18,19,20].) The main goal in this article is to extend our formulas from SL 2 (Z) to Γ 0 (N ).…”

Section: Introductionmentioning

confidence: 99%

“…(Note that periods and the Hecke operators on periods have been studied by a number of mathematicians. To name a few, see [1,5,8,12,14,15,17,18,19,20]. )…”

Section: Introductionmentioning

confidence: 99%

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Period polynomials and explicit formulas for Hecke operators on Γ₀(2)

Fukuhara¹,

Yang²

2009

Math. Proc. Camb. Phil. Soc.

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Let S w+2 (Γ 0 (N )) be the vector space of cusp forms of weight w + 2 on the congruence subgroup Γ 0 (N ). We first determine explicit formulas for period polynomials of elements in S w+2 (Γ 0 (N )) by means of Bernoulli polynomials. When N = 2, from these explicit formulas we obtain new bases for S w+2 (Γ 0 (2)), and extend the Eichler-Shimura-Manin isomorphism theorem to Γ 0 (2). This implies that there are natural correspondences between the spaces of cusp forms on Γ 0 (2) and the spaces of period polynomials. Based on these results, we will find explicit form of Hecke operators on S w+2 (Γ 0 (2)). As an application of our main theorems, we will also give an affirmative answer to a speculation of Imamoḡlu and Kohnen on a basis of S w+2 (Γ 0 (2)).2000 Mathematics Subject Classification. Primary 11F25; Secondary 11F11, 11F67.

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