Related papers: On the Rankin-Selberg method for higher genus stri…

We propose a formalism inspired by matrix models to compute open and closed topological string amplitudes in the B-model on toric Calabi-Yau manifolds. We find closed expressions for various open string amplitudes beyond the disk, and in…

We continue the study of a class of string-motivated effective supergravity theories in light of current data from the CERN Large Hadron Collider (LHC). In this installment we consider Type IIB string theory compactified on a Calabi-Yau…

We explore single and multi-loop conformal integrals, such as the ones appearing in dual conformal theories in flat space. Using Mellin amplitudes, a large class of higher loop integrals can be written as simple integro-differential…

By the unfolding method, Rankin-Selberg L-functions for ${\rm GL}(n)\times{\rm GL}(m)$ can be expressed in terms of period integrals. These period integrals actually define invariant forms on tensor products of the relevant automorphic…

We establish a sub-convexity estimate for Rankin-Selberg $L$-functions in the combined level aspect, using the circle method. If $p$ and $q$ are distinct prime numbers, $f$ and $g$ are non-exceptional newforms (modular or Maass) for the…

The method of sub-iteration, which was previously applied to the higher-order coupled cluster amplitude equations, is extended to the case of the coupled cluster $\Lambda$ equations. The sub-iteration procedure for the $\Lambda$ equations…

We study Fuglede's $p$-module of systems of measures in condensers in Euclidean spaces and on polarizable Carnot groups. We apply and generalize a result by Rodin, which provides an explicit method for finding the extremal function and the…

We provide new methods to straightforwardly obtain compact and analytic expressions for epsilon-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for…

We first develop theories of differential rings of quasi-Siegel modular and quasi-Siegel Jacobi forms for genus two. Then we apply them to the Eynard-Orantin topological recursion of certain local Calabi-Yau threefolds equipped with branes,…

We prove a vanishing theorem for one forms on the moduli stack of principally polarized abelian varieties of genus g>1 with level structure N over fields of characteristic p different from two. This is used to compute the Picard groups of…

We study the behavior of the effective potential between revolving D$p$-branes at all ranges of the distance $r$, interpolating $r \gg l_s$ and $r \ll l_s$ ($l_s$ is the string length). Since the one-loop open string amplitude cannot be…

We consider spaces of modular forms attached to definite orthogonal groups of low even rank and nontrivial level, equipped with Hecke operators defined by Kneser neighbours. After reviewing algorithms to compute with these spaces, we…

We find a Nekrasov-type expression for the Seiberg-Witten prepotential for the six-dimensional non-critical E_8 string theory toroidally compactified down to four dimensions. The prepotential represents the BPS partition function of the E_8…

We discuss intrinsic relaxation rates in superconductors, and how they may be measured using non-linear optical (terahertz) response. We consider both $s$ and $d$-wave superconductors, both with and without a phenomenological (energy…

We study celestial amplitudes in string theory at one-loop. Celestial amplitudes describe scattering processes of boost eigenstates and relate to amplitudes in the more standard basis of momentum eigenstates through a Mellin transform. They…

We employ multiparticle factorization to constrain deformations of tree-level open string amplitudes. Assuming minimal degeneracy among intermediate states of the same spin up through the second excited level, we find that the Regge…

We study the distribution, in the space of Satake parameters, of local components of Siegel cusp forms of genus 2 and growing weight, subject to a specific weighting which allows us to apply results concerning Bessel models and a variant of…

We investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. In the Tucker decomposition framework, we show that the Riemannian optimization algorithm with initial value…

For general one-matrix models in the large $N$ limit, we introduce the cap amplitude $\psi(b)$ as the expansion coefficient of the 1-form $ydx$ on the spectral curve. We find that the dilaton equation for the discrete volume $N_{g,n}$ of…

We provide efficient methods to evaluate the Riemann zeta, the Lerch zeta and the Dirichlet $L$-functions. The method uses the Riemann-Siegel (RS) type formulas and a modified double exponential (MDE) quadrature method near the saddle point…