195 citations · 402 across the 17 of their papers we have counts for
19 papers
Elliptic KZB connections via universal vector extensions
Tiago J. Fonseca, Nils Matthes
Using the formalism of bar complexes and their relative versions, we give a new, purely algebraic, construction of the so-called universal elliptic KZB connection in arbitrary leve…
Modular graph forms from equivariant iterated Eisenstein integrals
Daniele Dorigoni, Mehregan Doroudiani, Joshua Drewitt +5
The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differe…
The distribution of Manin's iterated integrals of modular forms
Nils Matthes, Morten S. Risager
We determine the asymptotic distribution of Manin's iterated integrals of length at most 2. For all lengths we compute all the asymptotic moments. We show that if the length is at…
A note on the Gauss-Manin connection for abelian schemes
Tiago J. Fonseca, Nils Matthes
We study differential forms on the universal vector extension of an abelian scheme in characteristic zero, and derive a new construction of the -group scheme st…
Meromorphic modular forms and the three-loop equal-mass banana integral
Johannes Broedel, Claude Duhr, Nils Matthes
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 mer…
Realizations of the formal double Eisenstein space
Henrik Bachmann, Ulf Kühn, Nils Matthes
We introduce the formal double Eisenstein space , which is a generalization of the formal double zeta space of Gangl-Kaneko-Zagier, and prove analogu…
Iterated primitives of meromorphic quasimodular forms for
Nils Matthes
We introduce and study iterated primitives of meromorphic quasimodular forms for , generalizing work of Manin and Brown for holomorphic modular form…
Towards algebraic iterated integrals on elliptic curves via the universal vectorial extension
Tiago J. Fonseca, Nils Matthes
For an elliptic curve defined over a field , we study iterated path integrals of logarithmic differential forms on , the universal vectorial exte…
An algebraic characterization of the Kronecker function
Nils Matthes
We characterize the generating series of extended period polynomials of normalized Hecke eigenforms for studied by Zagier in terms of the period r…
On Ecalle's and Brown's polar solutions to the double shuffle equations modulo products
Nils Matthes, Koji Tasaka
Two explicit sets of solutions to the double shuffle equations modulo products were introduced by Ecalle and Brown respectively. We place the two solutions into the same algebraic…
On the algebraic structure of iterated integrals of quasimodular forms
Nils Matthes
We study the algebra of iterated integrals of quasimodular forms for , which is the smallest extension of the algebra $QM_{\ast}…
Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes
Johannes Broedel, Nils Matthes, Gregor Richter +1
We consider a generalization of elliptic multiple zeta values, which we call twisted elliptic multiple zeta values. These arise as iterated integrals on an elliptic curve from whic…
Decomposition of elliptic multiple zeta values and iterated Eisenstein integrals
Nils Matthes
We describe a decomposition algorithm for elliptic multiple zeta values, which amounts to the construction of an injective map from the algebra of elliptic multiple zeta values…
Elliptic multizetas and the elliptic double shuffle relations
Pierre Lochak, Nils Matthes, Leila Schneps
We define an elliptic generating series whose coefficients, the elliptic multizetas, are related to the elliptic analogues of multiple zeta values introduced by Enriquez as the coe…
The meta-abelian elliptic KZB associator and periods of Eisenstein series
Nils Matthes
We compute the image of Enriquez' elliptic KZB associator in the (maximal) meta-abelian quotient of the fundamental Lie algebra of a once-punctured elliptic curve. Our main result…
Linear independence of indefinite iterated Eisenstein integrals
Nils Matthes
We prove linear independence of indefinite iterated Eisenstein integrals over the fraction field of the ring of formal power series . Our proof relies on a general…
Elliptic Double Zeta Values
Nils Matthes
We study an elliptic analogue of multiple zeta values, the elliptic multiple zeta values of Enriquez, which are the coefficients of the elliptic KZB associator. Originally defined…
Relations between elliptic multiple zeta values and a special derivation algebra
Johannes Broedel, Nils Matthes, Oliver Schlotterer
We investigate relations between elliptic multiple zeta values and describe a method to derive the number of indecomposable elements of given weight and length. Our method is based…
Elliptic multiple zeta values and one-loop superstring amplitudes
Johannes Broedel, Carlos R. Mafra, Nils Matthes +1
We investigate iterated integrals on an elliptic curve, which are a natural genus-one generalization of multiple polylogarithms. These iterated integrals coincide with the multiple…