| 1. |
- Berg, Marcus, 1973-, et al.
(author)
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Massive deformations of Maass forms and Jacobi forms
- 2021
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In: Communications in Number Theory and Physics. - : INTERNATIONAL PRESS. - 1931-4523 .- 1931-4531. ; 15:3, s. 575-603
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Journal article (peer-reviewed)abstract
- We define one-parameter "massive" deformations of Maass forms and Jacobi forms. This is inspired by descriptions of plane gravitational waves in string theory. Examples include massive Green's functions (that we write in terms of Kronecker-Eisenstein series) and massive modular graph functions.
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| 2. |
- D'Hoker, Eric, et al.
(author)
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Identities among higher genus modular graph tensors
- 2022
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In: Communications in Number Theory and Physics. - : INT PRESS BOSTON, INC. - 1931-4523 .- 1931-4531. ; 16:1, s. 35-74
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Journal article (peer-reviewed)abstract
- Higher genus modular graph tensors map Feynman graphs to functions on the Torelli space of genus-h compact Riemann surfaces which transform as tensors under the modular group Sp(2h, Z), thereby generalizing a construction of Kawazumi. An infinite family of algebraic identities between one-loop and tree-level modular graph tensors are proven for arbitrary genus and arbitrary tensorial rank. We also derive a family of identities that apply to modular graph tensors of higher loop order.
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| 3. |
- Fedosova, Ksenia, et al.
(author)
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Fourier expansions of vector-valued automorphic functions with non-unitary twists
- 2023
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In: Communications in Number Theory and Physics. - 1931-4531 .- 1931-4523. ; 17:1, s. 173-248
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Journal article (peer-reviewed)abstract
- We provide Fourier expansions of vector-valued eigenfunctions of the hyperbolic Laplacian that are twist-periodic in a horocycle direction. The twist may be given by any endomorphism of a finite-dimensional vector space; no assumptions on invertibility or unitarity are made. Examples of such eigenfunctions include vector-valued twisted automorphic forms of Fuchsian groups. We further provide a detailed description of the Fourier coefficients and explicitly identify each of their constituents, which intimately depend on the eigenvalues of the twisting endomorphism and the size of its Jordan blocks. In addition, we determine the growth properties of the Fourier coefficients.
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