Results 41 to 50 of about 55,203 (163)
MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS
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 +2 more
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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
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Non-holomorphic modular forms from zeta generators
Journal of High Energy PhysicsWe study non-holomorphic modular forms built from iterated integrals of holomorphic modular forms for SL(2, ℤ) known as equivariant iterated Eisenstein integrals.
Daniele Dorigoni +7 more
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ρ — Adic Analogues of Ramanujan Type Formulas for 1/π
Mathematics, 2013 Following Ramanujan’s work on modular equations and approximations of π, there are formulas for 1/π of the form [PLEASE CHECK FORMULA IN THE PDF] for d = 2, 3, 4, 6, where λd are singular values that correspond to elliptic curves with complex ...
Sarah Chisholm +4 more
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All-order differential equations for one-loop closed-string integrals and modular graph forms
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
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From Holonomy of the Ising Model Form Factors to n-Fold Integrals and the Theory of Elliptic Curves
Symmetry, Integrability and Geometry: Methods and Applications, 2007 We recall the form factors $f^(j)_{N,N}$ corresponding to the $lambda$-extension $C(N,N; lambda)$ of the two-point diagonal correlation function of the Ising model on the square lattice and their associated linear differential equations which exhibit ...
Salah Boukraa +3 more
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Computing Classical Modular Forms
, 2021 63 pages; minor edits, including a correction to Conjecture 8.5 ...
Best, Alex +10 more
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Open Mathematics, 2019 After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the ...
Eum Ick Sun, Jung Ho Yun
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Siegel modular forms and black hole entropy
Journal of High Energy Physics, 2017 We discuss the application of Siegel Modular Forms to Black Hole entropy counting. The role of the Igusa cusp form χ 10 in the D1D5P system is well-known, and its transformation properties are what allows precision microstate counting in this case.
Alexandre Belin +3 more
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New A 4 lepton flavor model from S 4 modular symmetry
Journal of High Energy Physics, 2020 We study a flavor model with A 4 symmetry which originates from S 4 modular group. In S 4 symmetry, Z 2 subgroup can be anomalous, and then S 4 can be violated to A 4.
Tatsuo Kobayashi +4 more
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