Results 31 to 40 of about 616,220 (283)

Arithmetic of generalized Dedekind sums and their modularity

Open Mathematics, 2018
Dedekind sums were introduced by Dedekind to study the transformation properties of Dedekind η function under the action of SL2(ℤ). In this paper, we study properties of generalized Dedekind sums si,j(p, q). We prove an asymptotic expansion of a function
Choi Dohoon, Jun Byungheup, Lee Jungyun, Lim Subong   +3 more
doaj   +1 more source

Modular forms in the spectral action of Bianchi IX gravitational instantons

Journal of High Energy Physics, 2019
We prove a modularity property for the heat kernel and the Seeley-deWitt coefficients of the heat kernel expansion for the Dirac-Laplacian on the Bianchi IX gravitational instantons.
Wentao Fan, Farzad Fathizadeh, Matilde Marcolli   +2 more
doaj   +1 more source

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

Modular Forms on the Double Half-Plane

, 2020
We formulate a notion of modular form on the double half-plane for half-integral weights and explain its relationship to the usual notion of modular form.
Duncan, John F. R., McGady, David A.
core   +1 more source

Bilateral series in terms of mixed mock modular forms

Journal of Inequalities and Applications, 2016
The number of strongly unimodal sequences of weight n is denoted by u ∗ ( n ) $u^{*}(n)$ . The generating functions for { u ∗ ( n ) } n = 1 ∞ $\{u^{*}(n)\}_{n=1}^{\infty}$ are U ∗ ( q ) = ∑ n = 1 ∞ u ∗ ( n ) q n $U^{*}(q)=\sum_{n=1}^{\infty}u^{*}(n)q^{n}$
Bin Chen, Haigang Zhou
doaj   +1 more source

Topological Modular Forms [PDF]

, 2014
DEFINITION 3.5. An integral modular form of weight n is a law associating to every pointed curve of genus 1 a section of wo" in a way compatible with base change.
Douglas, C, Francis, J, Henriques, A, Hill, M   +3 more
openaire   +2 more sources

Nadler’s Theorem on Incomplete Modular Space

Mathematics, 2021
This manuscript is focused on the role of convexity of the modular, and some fixed point results for contractive correspondence and single-valued mappings are presented.
Fatemeh Lael, Naeem Saleem, Liliana Guran, Monica Felicia Bota   +3 more
doaj   +1 more source

Generalized modular forms

Journal of Number Theory, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Knopp, Marvin, Mason, Geoffrey
openaire   +2 more sources

Meromorphic modular forms and the three-loop equal-mass banana integral

Journal of High Energy Physics, 2022
We consider a class of differential equations for multi-loop Feynman integrals which can be solved to all orders in dimensional regularisation in terms of iterated integrals of meromorphic modular forms.
Johannes Broedel, Claude Duhr, Nils Matthes   +2 more
doaj   +1 more source

Non-Perturbative Corrections and Modularity in N=1 Type IIB Compactifications [PDF]

, 2007
Non-perturbative corrections and modular properties of four-dimensional type IIB Calabi-Yau orientifolds are discussed. It is shown that certain non-perturbative alpha' corrections survive in the large volume limit of the orientifold and periodically ...
A. Klemm, A.D. Linde, C. Borcea, C. Voisin, D. Baumann ., D. Lüst, D. Maulik, F. Denef, F. Denef, For a review see, G. Smet, I. Brunner, K. Becker, K. Hori ., L. Görlich, M. Aganagic, M. Eichler, M. Mariño, M.-X. Huang, N. Halmagyi, N.J. Hitchin, P. Berglund, P.K. Tripathy, P.S. Aspinwall, R. Gopakumar, R. Gopakumar, S. Yamaguchi, T.W. Grimm, Thomas W Grimm, V. Balasubramanian, W. Barth   +30 more
core   +2 more sources