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Modular Forms and Weierstrass Mock Modular Forms [PDF]

Mathematics, 2016
Alfes, Griffin, Ono, and Rolen have shown that the harmonic Maass forms arising from Weierstrass ζ-functions associated to modular elliptic curves “encode” the vanishing and nonvanishing for central values and derivatives of twisted Hasse-Weil L ...
Amanda Clemm
doaj   +3 more sources

Mock modular forms as $p$-adic modular forms [PDF]

Transactions of the American Mathematical Society, 2010
In this paper, we consider the question of correcting mock modular forms in order to obtain $p$-adic modular forms. In certain cases we show that a mock modular form $M^+$ is a $p$-adic modular form.
Bringmann, Kathrin, Guerzhoy, Pavel, Kane, Ben   +2 more
core   +6 more sources

Slopes of modular forms

, 2016
We survey the progress (or lack thereof!) that has been made on some questions about the p-adic slopes of modular forms that were raised by the first author in [Buz05], discuss strategies for making further progress, and examine other related questions ...
Buzzard, Kevin, Gee, Toby
core   +2 more sources

Perfectoid Drinfeld Modular Forms [PDF]

Journal de théorie des nombres de Bordeaux, 2022
In the first part, we revisit Drinfeld modular curves associated to GL(2) from the perfectoid point of view, and we show how to recover (a perfectized) part of the theory of overconvergent π-adic Drinfeld modular forms. In the second part, we review open problems for families of Drinfeld modular forms for GL(n).
Nicole, Marc-Hubert, Rosso, Giovanni
openaire   +2 more sources

Seven Small Simple Groups Not Previously Known to Be Galois Over $\mathbb{Q}$

Mathematics, 2022
In this note we realize seven small simple groups as Galois groups over Q. The technique that we employ is the determination of the images of Galois representations attached to modular and automorphic forms, relying in two cases on recent results of ...
Luis Dieulefait, Enric Florit, Núria Vila   +2 more
doaj   +1 more source

On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds [PDF]

Royal Society Open Science, 2015
In this paper, we study modularity of several functions which naturally arose in a recent paper of Lau and Zhou on open Gromov–Witten potentials of elliptic orbifolds.
Kathrin Bringmann, Larry Rolen, Sander Zwegers   +2 more
doaj   +1 more source

Modular flavor symmetry and vector-valued modular forms

Journal of High Energy Physics, 2022
We revisit the modular flavor symmetry from a more general perspective. The scalar modular forms of principal congruence subgroups are extended to the vector-valued modular forms, then we have more possible finite modular groups including Γ N and Γ N ′ $$
Xiang-Gan Liu, Gui-Jun Ding
doaj   +1 more source

sl(2)ˆ decomposition of denominator formulae of some BKM Lie superalgebras

Nuclear Physics B, 2021
We study a family of Siegel modular forms that are constructed using Jacobi forms that arise in Umbral moonshine. All but one of them arise as the Weyl-Kac-Borcherds denominator formula of some Borcherds-Kac-Moody (BKM) Lie superalgebras.
Suresh Govindarajan, Mohammad Shabbir, Sankaran Viswanath   +2 more
doaj   +1 more source

4-manifolds and topological modular forms

Journal of High Energy Physics, 2021
We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds.
Sergei Gukov, Du Pei, Pavel Putrov, Cumrun Vafa   +3 more
doaj   +1 more source

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