Results 11 to 20 of about 1,658 (186)
Little string instanton partition functions and scalar propagators
Journal of High Energy Physics, 2023 We discuss a class of Little String Theories (LSTs) whose low energy descriptions are supersymmetric gauge theories on the Ω-background with gauge group U(N) and matter in the adjoint representation. We show that the instanton partition function of these
Baptiste Filoche, Stefan Hohenegger
doaj +1 more source
Two string theory flavours of generalised Eisenstein series
Journal of High Energy Physics, 2023 Generalised Eisenstein series are non-holomorphic modular invariant functions of a complex variable, τ, subject to a particular inhomogeneous Laplace eigenvalue equation on the hyperbolic upper-half τ-plane.
Daniele Dorigoni, Rudolfs Treilis
doaj +1 more source
On constant terms of Eisenstein series [PDF]
Acta Arithmetica, 2021 We calculate the constant terms of certain Hilbert modular Eisenstein series at all cusps. Our formula relates these constant terms to special values of Hecke $L$-series. This builds on previous work of Ozawa, in which a restricted class of Eisenstein series were studied. Our results have direct arithmetic applications---in separate work we apply these
Dasgupta, Samit, Kakde, Mahesh
openaire +3 more sources
Algorithms and tools for iterated Eisenstein integrals
Journal of High Energy Physics, 2020 We present algorithms to work with iterated Eisenstein integrals that have recently appeared in the computation of multi-loop Feynman integrals. These algorithms allow one to analytically continue these integrals to all regions of the parameter space ...
Claude Duhr, Lorenzo Tancredi
doaj +1 more source
Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series
Journal of High Energy Physics, 2018 We present a generalization of the symbol calculus from ordinary multiple polylogarithms to their elliptic counterparts. Our formalism is based on a special case of a coaction on large classes of periods that is applied in particular to elliptic ...
Johannes Broedel +4 more
doaj +1 more source
Relation between Borweins’ Cubic Theta Functions and Ramanujan’s Eisenstein Series
Journal of Applied Mathematics, 2021 Two-dimensional theta functions were found by the Borwein brothers to work on Gauss and Legendre’s arithmetic-geometric mean iteration. In this paper, some new Eisenstein series identities are obtained by using (p, k)-parametrization in terms of Borweins’
B. R. Srivatsa Kumar +2 more
doaj +1 more source
A fresh approach to classical Eisenstein series and the newer Hilbert–Eisenstein series [PDF]
International Journal of Number Theory, 2017 This paper is concerned with new results for the circular Eisenstein series [Formula: see text] as well as with a novel approach to Hilbert–Eisenstein series [Formula: see text], introduced by Michael Hauss in 1995. The latter turns out to be the product of the hyperbolic sinh function with an explicit closed form linear combination of digamma ...
Butzer, Paul L., Pogány, Tibor K.
openaire +3 more sources
A REMARK OF EISENSTEIN SERIES AND THETA SERIES [PDF]
Bulletin of the Korean Mathematical Society, 2002 The authors claim results of the kind \(\theta_3(\tau^2)^4= \theta_3(\tau)^4\), \(\Delta(\tau^2)= \Delta(\tau)\), \(J(\tau^2)= J(\tau)\) for some \(\tau\) in the upper half plane which belong to an imaginary quadratic number field. Here, \(\theta_3\) is the Jacobi theta function, \(\Delta\) is the modular discriminant, and \(J\) is the elliptic modular
Kim, Daeyeoul, Koo, Ja Kyung
openaire +2 more sources
One-loop open-string integrals from differential equations: all-order α′-expansions at n points
Journal of High Energy Physics, 2020 We study generating functions of moduli-space integrals at genus one that are expected to form a basis for massless n-point one-loop amplitudes of open superstrings and open bosonic strings.
Carlos R. Mafra, Oliver Schlotterer
doaj +1 more source
Eisenstein Series and String Thresholds [PDF]
Communications in Mathematical Physics, 2000 Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms renumbered, plus minor corrections; v3: relation (1.7) to math Eis series clarified, eq (3.3) and minor typos corrected, final version to appear in Comm. Math.
Obers, N. A., Pioline, B.
openaire +3 more sources