Three-loop contributions to the ρ parameter and iterated integrals of modular forms by Samuel Abreu, Matteo Becchetti, Claude Duhr, Robin Marzucca

“…We find that the results involve exactly the same class of functions that appears in the well-known sunrise and banana graphs, namely elliptic polylogarithms and iterated integrals of modular forms. Using recent developments in the understanding of these functions, we analytically continue all the iterated integrals of modular forms to all regions of the parameter space, and in each region we obtain manifestly real and fast-converging series expansions for these functions.…”
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Data for "An optimal uncertainty principle in twelve dimensions via modular forms" by Cohn, Henry, Gonçalves, Felipe

“…This data set includes all the numerical data referred to in the paper "An optimal uncertainty principle in twelve dimensions via modular forms" by Cohn and Gonçalves (available on the arXiv with arXiv ID 1712.04438, at the URL https://arXiv.org/abs/1712.04438).…”
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p-adic modular forms over Shimura curves over Q by Kassaei, Payman L., 1973-

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Computing mod ℓ Galois representations associated to modular forms for small primes by Peng Tian, Ha Thanh Nguyen Tran, Dung Hoang Duong

Subjects: “…modular forms…”
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A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS by FRANCIS BROWN

“…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 holomorphic Eisenstein series. …”
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Explicit construction of mock modular forms from weakly holomorphic Hecke eigenforms by Choi SoYoung, Kim Chang Heon

Subjects: “…mock modular forms…”
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Modular forms and SL(2, ℤ)-covariance of type IIB superstring theory by Michael B. Green, Congkao Wen

“…For p = 3 and n ≥ 6 there are two independent modular forms, one of which has a vanishing tree-level contribution. …”
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L-functions for meromorphic modular forms and sum rules in conformal field theory by David A. McGady

“…When a modular form has an order-p pole away from cusps, its q-series coefficients grow as n p−1 e 2πnt for t ≥ 3 2 $$ t\ge \frac{\sqrt{3}}{2} $$ . …”
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Data for "Dual linear programming bounds for sphere packing via modular forms" by Cohn, Henry, Triantafillou, Nicholas

“…This data set contains numerical data for the paper "Dual linear programming bounds for sphere packing via modular forms" by Cohn and Triantafillou (available on the arXiv with arXiv ID 1909.04772, at the URL https://arXiv.org/abs/1909.04772).…”
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Algebraic de Rham theory for weakly holomorphic modular forms of level one by Brown, F, Hain, R

“…We establish an Eichler–Shimura isomorphism for weakly modular forms of level one. We do this by relating weakly modular forms with rational Fourier coefficients to the algebraic de Rham cohomology of the modular curve with twisted coefficients. …”

A class of nonholomorphic modular forms II: equivariant iterated Eisenstein integrals by Brown, FCS

“…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 holomorphic Eisenstein series. …”

Non-zero coefficients of half-integral weight modular forms mod ℓ by Bellaïche, J, Green, BJ, Soundararajan, K

“…We obtain new lower bounds for the number of Fourier coefficients of a weakly holomorphic modular form of half-integral weight not divisible by some prime $\ell$. …”

Siegel's modular forms and Dirichlet series : course given at the University of Maryland, 1969-1970 / by 316164 Maab, Hans

$G$-fixed Hilbert schemes on $K3$ surfaces, modular forms, and eta products by Jim Bryan, Ádám Gyenge

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STARK POINTS AND $p$-ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE by HENRI DARMON, ALAN LAUDER, VICTOR ROTGER

“…Fast algorithms for computing $p$-adic iterated integrals based on Katz expansions of overconvergent modular forms are then exploited to gather numerical evidence in more exotic scenarios, encompassing Mordell–Weil groups over cyclotomic fields, ring class fields of real quadratic fields (a setting which may shed light on the theory of Stark–Heegner points attached to Shintani-type cycles on ${\mathcal{H}}_{p}\times {\mathcal{H}}$), and extensions of $\mathbb{Q}$ with Galois group a central extension of the dihedral group $D_{2n}$ or of one of the exceptional subgroups $A_{4}$, $S_{4}$, and $A_{5}$ of $\mathbf{PGL}_{2}(\mathbb{C})$.…”
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Stark points and p-adic iterated integrals attached to modular forms of weight one by Lauder, A, Darmon, H, Rotger, V

“…Fast algorithms for computing p-adic iterated integrals based on Katz expansions of overconvergent modular forms are then exploited to gather numerical evidence in more exotic scenarios, encompassing Mordell–Weil groups over cyclotomic fields, ring class fields of real quadratic fields (a setting which may shed light on the theory of Stark–Heegner points attached to Shintani-type cycles on Hp×H), and extensions of Q with Galois group a central extension of the dihedral group D2n or of one of the exceptional subgroups A4, S4, and A5 of PGL2(C).…”

The three-loop equal-mass banana integral in ε-factorised form with meromorphic modular forms by Sebastian Pögel, Xing Wang, Stefan Weinzierl

“…Abstract We show that the differential equation for the three-loop equal-mass banana integral can be cast into an ε-factorised form with entries constructed from (meromorphic) modular forms and one special function, which can be given as an iterated integral of meromorphic modular forms. …”
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Gross-Stark units and p-adic iterated integrals attached to modular forms of weight one by Lauder, A, Darmon, H, Rotger, V

Modular forms of half-integral weight on Γ0(4) with few nonvanishing coefficients modulo ℓ by Choi Dohoon, Lee Youngmin

Subjects: “…fourier coefficients of modular forms…”
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Overconvergent modular forms are highest-weight vectors in the Hodge-Tate weight zero part of completed cohomology by Sean Howe

“…We construct a $(\mathfrak {gl}_2, B(\mathbb {Q}_p))$ and Hecke-equivariant cup product pairing between overconvergent modular forms and the local cohomology at $0$ of a sheaf on $\mathbb {P}^1$, landing in the compactly supported completed $\mathbb {C}_p$-cohomology of the modular curve. …”
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