Lifting of vector-valued automorphic forms
Jitendra Bajpai1 ; Subham Bhakta2
1 Department of Mathematics, Kiel University Heinrich-Hecht-Platz 6 24118 Kiel, Germany
2 Department of Mathematics, Indian Institute of Science Education and Research Thiruvananthapuram Kerala 695551, India
Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 3, pp. 843-867.

A recent study by the first author [2] demonstrated that admissible vector-valued automorphic forms have admissible lifts. In this article, we study the specific case of logarithmic vector-valued automorphic forms, exploring their lifts and providing explicit computations of their Fourier coefficients.

Dans un article récent [2], le premier auteur a démontré que les formes automorphes vectorielles admissibles admettent des relèvements admissibles. Dans cet article, nous étudions le cas spécial des formes automorphes vectorielles logarithmiques, en étudiant leurs relèvements et en donnant des calculs explicites de leurs coefficients de Fourier.

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DOI : 10.5802/jtnb.1298
Classification : 11F03, 11F55, 30F35
Mots-clés : Fuchsian groups, automorphic forms, Fourier coefficients

Jitendra Bajpai 1 ; Subham Bhakta 2

1 Department of Mathematics, Kiel University Heinrich-Hecht-Platz 6 24118 Kiel, Germany
2 Department of Mathematics, Indian Institute of Science Education and Research Thiruvananthapuram Kerala 695551, India
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Jitendra Bajpai; Subham Bhakta. Lifting of vector-valued automorphic forms. Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 3, pp. 843-867. doi : 10.5802/jtnb.1298. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1298/

[1] Jitendra Bajpai On vector valued automorphic forms, Ph. D. Thesis, University of Alberta (Canada) (2015) (advisor: Terry Gannon)

[2] Jitendra Bajpai Lifting of Modular Forms, Publ. Math. Besançon, Algèbre Théorie Nombres, Volume 2019 (2019) no. 1, pp. 5-20 | DOI | Numdam | Zbl

[3] Jitendra Bajpai; Subham Bhakta; Renan Finder Growth of Fourier coefficients of vector-valued automorphic forms, J. Number Theory, Volume 249 (2023), pp. 237-273 | DOI | MR | Zbl

[4] Luca Candelori; Tucker Hartland; Christopher Marks; Diego Yépez Indecomposable vector-valued modular forms and periods of modular curves, Res. Number Theory, Volume 4 (2018) no. 2, 17, 24 pages | DOI | MR | Zbl

[5] Terry Gannon The theory of vector-valued modular forms for the modular group, Conformal field theory, automorphic forms and related topics (Contributions in Mathematical and Computational Sciences), Volume 8, Springer, 2014, pp. 247-286 | DOI | MR | Zbl

[6] Marvin Knopp; Geoffrey Mason Logarithmic vector-valued modular forms, Acta Arith., Volume 147 (2011) no. 3, pp. 261-282 | DOI | MR | Zbl

[7] Marvin Knopp; Geoffrey Mason Logarithmic vector-valued modular forms and polynomial-growth estimates of their Fourier coefficients, Ramanujan J., Volume 29 (2012) no. 1-3, pp. 213-223 | DOI | MR | Zbl

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