Results 11 to 20 of about 80,487 (265)

Poisson equations for elliptic modular graph functions

Physics Letters B, 2021
We obtain Poisson equations satisfied by elliptic modular graph functions with four links. Analysis of these equations leads to a non–trivial algebraic relation between the various graphs.
Anirban Basu
doaj   +1 more source

Introductory remarks on complex multiplication

International Journal of Mathematics and Mathematical Sciences, 1982
Complex multiplication in its simplest form is a geometric tiling property. In its advanced form it is a unifying motivation of classical mathematics from elliptic integrals to number theory; and it is still of active interest.
Harvey Cohn
doaj   +1 more source

Some Modular Relations Analogues to the Ramanujan’s Forty Identities with Its Applications to Partitions

Axioms, 2013
Recently, the authors have established a large class of modular relations involving the Rogers-Ramanujan type functions J(q) and K(q) of order ten. In this paper, we establish further modular relations connecting these two functions with Rogers-Ramanujan
Nasser Abdo Saeed Bulkhali, Chandrashekar Adiga   +1 more
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Mathieu moonshine and Siegel Modular Forms

Journal of High Energy Physics, 2021
A second-quantized version of Mathieu moonshine leads to product formulae for functions that are potentially genus-two Siegel Modular Forms analogous to the Igusa Cusp Form. The modularity of these functions do not follow in an obvious manner.
Suresh Govindarajan, Sutapa Samanta
doaj   +1 more source

Weighted modular inequalities for monotone functions

Journal of Inequalities and Applications, 1997
Weight characterizations of weighted modular inequalities for operators on the cone of monotone functions are given in terms of composition operators on arbitrary non-negative functions with changes in weights. The results extend to modular inequalities,
Heinig HP, Kufner A, Drábek P
doaj   +2 more sources

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

Koshliakov zeta functions I: Modular relations [PDF]

Advances in Mathematics, 2021
34 pages, submitted for publication; comments are ...
Dixit, Atul, Gupta, Rajat
openaire   +2 more sources

Minimal Polynomials of Some Eta-Quotients Evaluated at CM Points

Mathematics
We study certain eta-quotients of weight zero evaluated at CM points of imaginary quadratic orders. Using the theory of extended form class groups, we show that these special values generate the corresponding ring class fields and we provide explicit ...
Ho Yun Jung
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Modular Quasi-Pseudo Metrics and the Aggregation Problem

Mathematics
The applicability of the distance aggregation problem has attracted the interest of many authors. Motivated by this fact, in this paper, we face the modular quasi-(pseudo-)metric aggregation problem, which consists of analyzing the properties that a ...
Maria del Mar Bibiloni-Femenias, Oscar Valero   +1 more
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A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS

Forum of Mathematics, Sigma, 2020
We introduce a new family of real-analytic modular forms on the upper-half plane. They are arguably the simplest class of ‘mixed’ versions of modular forms of level one and are constructed out of real and imaginary parts of iterated integrals of ...
FRANCIS BROWN
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