Divisors of modular forms on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>Γ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>

Atkinson, James R.

doi:10.1016/j.jnt.2004.07.014

Cited by 6 publications

(1 citation statement)

References 6 publications

(9 reference statements)

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“…To determine the derivatives of modular forms relative to the Hecke congruence subgroups is somewhat involved and has only recently been completed for the groups of genus zero that are of interest in the present paper [57][58][59]. In the interest of simplicity we focus in the following on groups of prime level, even though the analysis can be generalized to the remaining groups at the cost of more complicated formulae.…”

Section: Derivatives Of the Inflaton Potentialmentioning

confidence: 99%

Modular inflation at higher levelN

Lynker

Schimmrigk

2019

J. Cosmol. Astropart. Phys.

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We introduce the framework of modular inflation with level structure, generalizing the level one theory considered previously to higher levels. We analyze the modular structure of CMB observables in this framework and show that the nontrivial geometry of the target space suffices to ensure the almost holomorphic modularity of the relevant parameters. We further introduce a concrete class of models based on hauptmodul functions that provide generators of the corresponding inflationary potentials at level N > 1. The phenomenology of this class of models provides targets for ground-based CMB experiments in the immediate future. In the framework of our models we also discuss the status of the quantum gravity conjectures that have been formulated in the context of the swampland.

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Section: Derivatives Of the Inflaton Potentialmentioning

confidence: 99%

Modular inflation at higher levelN

Lynker

Schimmrigk

2019

J. Cosmol. Astropart. Phys.

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On Fourier Coefficients of Modular Forms

Cummins¹,

Haghighi²

2010

Bull. Aust. Math. Soc.

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In this paper we generalize these results and find recursive formulae for the Fourier coefficients of any meromorphic modular form f on any genuszero group commensurable with SL(2, Z), including noncongruence groups and expansions at irregular cusps. The form of the recurrence relations is well suited for the computation of the Fourier coefficients of the functions and forms on the groups which occur in monstrous and generalized moonshine. The required initial data has, in many cases, been computed by Norton (private communication).2010 Mathematics subject classification: primary 11F30; secondary 11F12, 11F03.

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The action of the heat operator on Jacobi forms

Richter

2008

Proc. Amer. Math. Soc.

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Divisors of modular forms on Γ0(4)

Cited by 6 publications

References 6 publications

Modular inflation at higher levelN

Modular inflation at higher levelN

On Fourier Coefficients of Modular Forms

The action of the heat operator on Jacobi forms

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