Results 51 to 60 of about 55,203 (163)

From modular graph forms to iterated integrals

Journal of High Energy Physics
Modular graph forms are a class of non-holomorphic modular forms that arise in the low-energy expansion of genus-one closed string amplitudes. In this work, we introduce a systematic procedure to convert lattice-sum representations of modular graph forms
E. Claasen, M. Doroudiani
doaj   +1 more source

Modular forms for three-loop banana integrals

Journal of High Energy Physics
We study periods of multi-parameter families of K3 surfaces, which are relevant to compute the maximal cuts of certain classes of Feynman integrals. We focus on their automorphic properties, and we show that generically the periods define orthogonal ...
Claude Duhr
doaj   +1 more source

HOLOMORPHIC ALMOST MODULAR FORMS [PDF]

Bulletin of the London Mathematical Society, 2004
Holomorphic almost modular forms are holomorphic functions of the complex upper half plane which can be approximated arbitrarily well (in a suitable sense) by modular forms of congruence subgroups of large index in $\SL(2,\ZZ)$. It is proved that such functions have a rotation-invariant limit distribution when the argument approaches the real axis.
openaire   +4 more sources

Definite orthogonal modular forms: computations, excursions, and discoveries. [PDF]

Res Number Theory, 2022
Assaf E, Fretwell D, Ingalls C, Logan A, Secord S, Voight J.   +5 more
europepmc   +1 more source

Interlacing of zeros of weakly holomorphic modular forms

Proceedings of the American Mathematical Society, Series B, 2014
We prove that the zeros of a family of extremal modular forms interlace, settling a question of Nozaki. Additionally, we show that the zeros of almost all forms in a basis for the space of weakly holomorphic modular forms of
Paul Jenkins, Kyle Pratt
doaj   +1 more source

Modular forms and hierarchical Yukawa couplings in heterotic Calabi-Yau compactifications

Journal of High Energy Physics
We study the modular symmetry in heterotic string theory on Calabi-Yau threefolds. In particular, we examine whether moduli-dependent holomorphic Yukawa couplings are described by modular forms in the context of heterotic string theory with standard ...
Keiya Ishiguro, Tatsuo Kobayashi, Satsuki Nishimura, Hajime Otsuka   +3 more
doaj   +1 more source

Plea for Diagonals and Telescopers of Rational Functions

Universe
This paper is a plea for diagonals and telescopers of rational or algebraic functions using creative telescoping, using a computer algebra experimental mathematics learn-by-examples approach. We show that diagonals of rational functions (and this is also
Saoud Hassani, Jean-Marie Maillard, Nadjah Zenine   +2 more
doaj   +1 more source

Modular inflation observables and j-inflation phenomenology

Journal of High Energy Physics, 2017
Modular inflation is the restriction to two fields of automorphic inflation, a general group based framework for multifield scalar field theories with curved target spaces, which can be parametrized by the comoving curvature perturbation ℛ and the ...
Rolf Schimmrigk
doaj   +1 more source

Linear relations between modular forms for Г0+(p)

Open Mathematics, 2015
We find linear relations among the Fourier coefficients of modular forms for the group Г0+(p) of genus zero. As an application of these linear relations, we derive congruence relations satisfied by the Fourier coefficients of normalized Hecke eigenforms.
Choi SoYoung, Kim Chang Heon
doaj   +1 more source

Non-holomorphic modular flavor symmetry

Journal of High Energy Physics
The formalism of non-holomorphic modular flavor symmetry is developed, and the Yukawa couplings are level N polyharmonic Maaß forms satisfying the Laplacian condition.
Bu-Yao Qu, Gui-Jun Ding
doaj   +1 more source