Results 101 to 110 of about 52,325 (233)

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

Modular invariant gluon-graviton scattering in AdS at one loop

Journal of High Energy Physics
We consider mixed gluon-graviton scattering in Type IIB string theory on AdS5 × S 5/ℤ 2 in the presence of D7 branes, which is dual to a mixed correlator of the SO(8) and SU(2) L flavor multiplets of a certain 4d N $$ \mathcal{N} $$ = 2 USp(2N) gauge ...
Shai M. Chester, Pietro Ferrero, Daniele R. Pavarini   +2 more
doaj   +1 more source

All modular forms of weight 2 can be expressed by Eisenstein series [PDF]

, 2020
Martin Raum, Jiacheng Xia
openalex   +1 more source

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

A construction of residues of Eisenstein series and relatedsquare-integrable classes in the cohomology of arithmetic groups of low k-rank [PDF]

, 2019
Neven Grbac, Joachim Schwermer
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

The Chowla-Selberg Method for Fourier Expansion of Higher Rank Eisenstein Series [PDF]

, 1985
Audrey Terras
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

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