Results 101 to 110 of about 52,441 (236)

Higher d Eisenstein series and a duality-invariant distance measure

Journal of High Energy Physics
The Petersson inner product is a natural inner product on the space of modular invariant functions. We derive a formula, written as a convergent sum over elementary functions, for the inner product E s (G, B) of the real analytic Eisenstein series $${E}_{
Nathan Benjamin, A. Liam Fitzpatrick
doaj   +1 more source

Explicit calculations with Eisenstein series [PDF]

, 2018
Matthew P. Young
openalex   +1 more source

Modular graph functions and odd cuspidal functions. Fourier and Poincaré series

Journal of High Energy Physics, 2019
Modular graph functions are SL(2, ℤ)-invariant functions associated with Feynman graphs of a two-dimensional conformal field theory on a torus of modulus τ. For one-loop graphs they reduce to real analytic Eisenstein series. We obtain the Fourier series,
Eric D’Hoker, Justin Kaidi
doaj   +1 more source

Eisenstein series for higher-rank groups and string theory amplitudes [PDF]

, 2010
Michael Green, Stephen D. Miller, Jorge G. Russo, Pierre Vanhove   +3 more
openalex   +1 more source

Deformations of Theta Integrals and A Conjecture of Gross-Zagier

Forum of Mathematics, Sigma
In this paper, we complete the proof of the conjecture of Gross and Zagier concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an analogue of the incoherent Eisenstein series over
Jan H. Bruinier, Yingkun Li, Tonghai Yang   +2 more
doaj   +1 more source

Fourier coefficients of Eisenstein series of one complex variable for the special linear group [PDF]

, 1975
Audrey Terras
openalex   +1 more source

Transformation formulas for the higher power of odd zeta values and generalized Eisenstein series [PDF]

, 2022
Soumyarup Banerjee, Vijay Sahani
openalex   +1 more source

Integral Transforms in Number Theory

Axioms
Integral transforms play a fundamental role in science and engineering. Above all, the Fourier transform is the most vital, which has some specifications—Laplace transform, Mellin transform, etc., with their inverse transforms. In this paper, we restrict
Guodong Liu, Takako Kuzumaki, Shigeru Kanemitsu   +2 more
doaj   +1 more source

Cancellation of divergences up to three loops in exceptional field theory

Journal of High Energy Physics, 2018
We consider the tetrahedral three-loop diagram in E d exceptional field theory evaluated as a scalar diagram for four external gravitons. At lowest order in momenta, this diagram contributes to the ∇6 R 4 term in the low-energy effective action for M ...
Guillaume Bossard, Axel Kleinschmidt
doaj   +1 more source

Hecke eigenvalues and relations for degree 2 Siegel Eisenstein series [PDF]

, 2011
Lynne H. Walling
openalex   +1 more source