Results 1 to 10 of about 12,945,827 (295)
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 +6 more sources
Modular flavor symmetry and vector-valued modular forms [PDF]
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 +2 more sources
Meromorphic modular forms and the three-loop equal-mass banana integral [PDF]
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 +2 more
doaj +2 more sources
4-manifolds and topological modular forms [PDF]
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 +3 more
doaj +2 more sources
On a q-deformation of modular forms [PDF]
Journal of Mathematical Analysis and Applications, 2018 There are many instances known when the Fourier coefficients of modular forms are congruent to partial sums of hypergeometric series. In our previous work, such partial sums are related to the radial asymptotics of infinite q-hypergeometric sums at roots
Victor J. W. Guo, W. Zudilin
semanticscholar +6 more sources
On Divisors of Modular Forms [PDF]
Advances in Mathematics, 2016 The denominator formula for the Monster Lie algebra is the product expansion for the modular function $j(z)-j(\tau)$ given in terms of the Hecke system of $\operatorname{SL}_2(\mathbb Z)$-modular functions $j_n(\tau)$. It is prominent in Zagier's seminal
Kathrin Bringmann +4 more
semanticscholar +6 more sources
On quasi-modular forms, almost holomorphic modular forms, and the vector-valued modular forms of Shimura [PDF]
Ramanujan Journal, 2014 17 pages, minor ...
exaly +4 more sources
A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS
Forum of Mathematics, Sigma, 2020 We introduce a new family of real-analytic modular forms on the upper-half plane. They are arguably the simplest class of ‘mixed’ versions of modular forms of level one and are constructed out of real and imaginary parts of iterated integrals of ...
FRANCIS BROWN
doaj +2 more sources
All-order differential equations for one-loop closed-string integrals and modular graph forms [PDF]
Journal of High Energy Physics, 2020 We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and type-II theories.
Jan E. Gerken +2 more
doaj +2 more sources
A -expansions of Drinfeld modular forms
Journal of Number Theory, 2013 This version does not use normalized Goss polynomials, which fixes various inaccuracies in the previous ...
exaly +3 more sources