Results 21 to 30 of about 477,721 (333)

Modular divisor functions and quadratic reciprocity [PDF]

, 2010
It is a well-known result by B. Riemann that the terms of a conditionally convergent series of real numbers can be rearranged in a permutation such that the resulting series converges to any prescribed sum s: add p1 consecutive positive terms until their
Steiner, R.
core   +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
doaj   +1 more source

Asymptotic expansions, $L$-values and a new Quantum Modular Form [PDF]

, 2013
In 2010 Zagier introduced the notion of a quantum modular form. One of his first examples was the "strange" function $F(q)$ of Kontsevich. Here we produce a new example of a quantum modular form by making use of some of Ramanujan's mock theta functions ...
Costa, Edgar, Debaene, Korneel, Guerreiro, João   +2 more
core   +3 more sources

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

Higher Coxeter graphs associated to affine su(3) modular invariants [PDF]

, 2005
The affine $su(3)$ modular invariant partition functions in 2d RCFT are associated with a set of generalized Coxeter graphs. These partition functions fall into two classes, the block-diagonal (Type I) and the non block-diagonal (Type II) cases ...
Hammaoui, D., Schieber, G., Tahri, E. H.
core   +2 more sources

Polar harmonic Maass forms and their applications [PDF]

, 2016
In this survey, we present recent results of the authors about non-meromorphic modular objects known as polar harmonic Maass forms. These include the computation of Fourier coefficients of meromorphic modular forms and relations between inner products of
Bringmann, Kathrin, Kane, Ben
core   +2 more sources

A Framework for Modular Properties of False Theta Functions

, 2019
False theta functions closely resemble ordinary theta functions, however they do not have the modular transformation properties that theta functions have.
Bringmann, Kathrin, Nazaroglu, Caner
core   +1 more source