Results 61 to 70 of about 118 (89)

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

Towards motivic coactions at genus one from zeta generators

Journal of High Energy Physics
The motivic coaction of multiple zeta values and multiple polylogarithms encodes both structural insights on and computational methods for scattering amplitudes in a variety of quantum field theories and in string theory.
Axel Kleinschmidt, Franziska Porkert, Oliver Schlotterer   +2 more
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

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

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

Co-rank 1 $1$ 1 Arithmetic Siegel–Weil IV: Analytic local-to-global

Forum of Mathematics, Sigma
This is the fourth in a sequence of four papers, where we prove the arithmetic Siegel–Weil formula in co-rank 1 $1$ 1 for Kudla–Rapoport special cycles on exotic smooth integral models of unitary Shimura varieties of arbitrarily large even ...
Ryan Chen
doaj   +1 more source

The global Gan-Gross-Prasad conjecture for unitary groups. II. From Eisenstein series to Bessel periods

Forum of Mathematics, Pi
We state and prove an extension of the global Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture to the case of some Eisenstein series on unitary groups $U_n\times U_{n+1}$ .
Raphaël Beuzart-Plessis, Pierre-Henri Chaudouard   +1 more
doaj   +1 more source

A Tapestry of Ideas with Ramanujan’s Formula Woven In

Axioms
Zeta-functions play a fundamental role in many fields where there is a norm or a means to measure distance. They are usually given in the forms of Dirichlet series (additive), and they sometimes possess the Euler product (multiplicative) when the domain ...
Nianliang Wang, Takako Kuzumaki, Shigeru Kanemitsu   +2 more
doaj   +1 more source

Holographic thermal propagator from modularity

Journal of High Energy Physics
It is known that the holographic thermal propagator in 4 spacetime dimensions can be related to the Nekrasov-Shatashvili limit of the Ω-deformed $$\mathcal{N}=2$$ supersymmetric SU(2) Yang-Mills theory with N f = 4 hypermultiplets.
Borut Bajc, Katarina Trailović
doaj   +1 more source

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p-adic Siegel–Eisenstein series of degree two

Journal of Number Theory, 2012
Sho Takemori
exaly