Results 91 to 100 of about 50,891 (201)

Hankel Determinants of Eisenstein Series [PDF]

, 2001
In this paper we prove Garvan's conjectured formula for the square of the modular discriminant $ $ as a 3 by 3 Hankel determinant of classical Eisenstein series $E_{2n}$. We then obtain similar formulas involving minors of Hankel determinants for $E_{2r} ^m$, for $m=1,2,3$ and $r=2,3,4,5,7$, and $E_{14} ^4$.
openaire   +2 more sources

Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8

Open Mathematics
In this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered.
Jin Seokho, Park Ho
doaj   +1 more source

On the local $L^2$ -Bound of the Eisenstein series

Forum of Mathematics, Sigma
We study the growth of the local $L^2$ -norms of the unitary Eisenstein series for reductive groups over number fields, in terms of their parameters. We derive a poly-logarithmic bound on an average, for a large class of reductive groups.
Subhajit Jana, Amitay Kamber
doaj   +1 more source

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

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

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

Slapstick Classicism: Chaplin among the Sculptures

Critical Quarterly, Volume 67, Issue 4, Page 42-64, December 2025.
James Reath
wiley   +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

Chaplin's Nuts

Critical Quarterly, Volume 67, Issue 4, Page 121-135, December 2025.
Mark Steven
wiley   +1 more source