Results 1 to 10 of about 480,606 (330)

Modular Graph Functions [PDF]

Communications in Number Theory and Physics, 2016
In earlier work we studied features of non-holomorphic modular functions associated with Feynman graphs for a conformal scalar field theory on a two-dimensional torus with zero external momenta at all vertices.
D'Hoker, Eric, Green, Michael B., Gurdogan, Omer, Vanhove, Pierre   +3 more
core   +6 more sources

Modular forms, hypergeometric functions and congruences [PDF]

, 2013
Using the theory of Stienstra and Beukers, we prove various elementary congruences for the numbers \sum \binom{2i_1}{i_1}^2\binom{2i_2}{i_2}^2...\binom{2i_k}{i_k}^2, where k,n \in N, and the summation is over the integers i_1, i_2, ...i_k >= 0 such that ...
Matija Kazalicki
openalex   +3 more sources

MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS [PDF]

Forum of Mathematics, Pi, 2013
Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function $f(q)$, Ramanujan claims that as $q$ approaches an even-order $2k$ root of unity, we have $$\begin{eqnarray ...
AMANDA FOLSOM, KEN ONO, ROBERT C. RHOADES   +2 more
doaj   +2 more sources

Lessons from the Ramond sector [PDF]

SciPost Physics, 2020
We revisit the consistency of torus partition functions in (1+1)$d$ fermionic conformal field theories, combining traditional ingredients of modular invariance/covariance with a modernized understanding of bosonization/fermionization dualities.
Nathan Benjamin, Ying-Hsuan Lin
doaj   +5 more sources

Modular Equations and Distortion Functions [PDF]

The Ramanujan Journal, 2007
Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings.
B.C. Berndt, B.C. Berndt, C.-Q. He, D. Partyka, D. Partyka, E.T. Whittaker, F. Bowman, G. D. Anderson, G. Martin, G.D. Anderson, G.D. Anderson, G.D. Anderson, G.D. Anderson, G.D. Anderson, J. Hempel, J. Hersch, J. Jenkins, J. Väisälä, J. Väisälä, J. Zaja̧c, J.M. Borwein, M. Vuorinen, M. Vuorinen, M. Vuorinen, M.K. Vamanamurthy, O. Lehto, O. Lehto, P. Seittenranta, P. Tukia, P.F. Byrd, P.P. Belinskii, S. Agard, S. Agard, S. Yamashita, S. Zhang, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, W.K. Hayman, W.K. Hayman, Z. Li   +45 more
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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   +2 more sources

Modular properties of massive scalar partition functions [PDF]

Journal of High Energy Physics
We compute the exact thermal partition functions of a massive scalar field on flat spacetime backgrounds of the form ℝ d−q × 𝕋 q+1 and show that they possess an SL(q + 1, ℤ) symmetry.
Ankit Aggarwal, Glenn Barnich
doaj   +2 more sources

Modular relations for the Rogers-Ramanujan-Slater type functions of order fifteen and its applications to partitions [PDF]

Romanian Journal of Mathematics and Computer Science, 2013
In a manuscript of Ramanujan, published with his Lost Notebook [20] there are forty identities involving the Rogers-Ramanujan functions. In this paper, we establish several modular relations involving the Rogers-Ramanujan functions and the Rogers ...
Chandrashekar Adiga, A. Vanitha, Nasser Abdo Saeed Bulkhali   +2 more
doaj   +1 more source

Robust H_∞ Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions

Mathematical and Computational Applications, 2021
In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO ...
Ahmad Taher Azar, Fernando E. Serrano, Nashwa Ahmad Kamal   +2 more
doaj   +1 more source

Class fields generated by coordinates of elliptic curves

Open Mathematics, 2022
Let KK be an imaginary quadratic field different from Q(−1){\mathbb{Q}}\left(\sqrt{-1}) and Q(−3){\mathbb{Q}}\left(\sqrt{-3}). For a nontrivial integral ideal m{\mathfrak{m}} of KK, let Km{K}_{{\mathfrak{m}}} be the ray class field modulo m{\mathfrak{m}}.
Jung Ho Yun, Koo Ja Kyung, Shin Dong Hwa
doaj   +1 more source