Related papers: On the residue method for period integrals

Complex periods are algebraic integrals over complex algebraic domains, also appearing as Feynman integrals and multiple zeta values. The Grothendieck-de Rham period isomorphisms for p-adic algebraic varieties defined via Monski-Washnitzer…

Using the Berline-Vergne integration formula for equivariant cohomology for torus actions, we prove that integrals over Grassmannians (classical, Lagrangian or orthogonal ones) of characteristic classes of the tautological bundle, can be…

If one has to attain high accuracy over long timescales during the numerical computation of the N-body problem, the method called Lie-integration is one of the most effective algorithms. In this paper we present a set of recurrence…

We define a period map for classical Campedelli surfaces, using a covering trick as in the case of Enriques surfaces: the period map is shown to come from a family of Enriques surfaces, obtained as quotients of the Campedelli surface by an…

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…

Period polynomials have long been fruitful tools for the study of values of $L$-functions in the context of major outstanding conjectures. In this paper, we survey some facets of this study from the perspective of Eichler cohomology. We…

Using the orbit method we attempt to reveal geometric and algebraic meaning of separation of variables for the integrable systems on coadjoint orbits in an $\mathfrak{sl}(3)$ loop algebra. We consider two types of generic orbits embedded…

We describe how to find period integrals and Picard-Fuchs differential equations for certain one-parameter families of Calabi-Yau manifolds. These families can be seen as varieties over a finite field, in which case we show in an explicit…

Let K be a complete discretely valued field with perfect residue field k. Assuming upper bounds on the relation between period and index for WC-groups over k, we deduce corresponding upper bounds on the relation between period and index for…

We extend Lax-Phillips' theorem on discreteness of pseudo-cuspforms, in the style of Colin de Verdi{\`e}re's use of the Friedrichs self-adjoint extension of a restriction of the Laplace-Beltrami operator, as opposed to the use of semigroup…

Characteristic modes of arbitrary two-dimensional periodic systems are analyzed using scattering parameter data. This approach bypasses the need for periodic integral equations and allows for characteristic modes to be computed from generic…

This paper introduces the notion of locally algebraic representations and corresponding sheaves in the context of the cohomology of arithmetic groups. These representations are of relevance for the study of integral structures and special…

We define certain higher-dimensional Dedekind sums that generalize the classical Dedekind-Rademacher sums, and show how to compute them effectively using a generalization of the continued-fraction algorithm. We present two applications.…

Through classical modularity conjectures, the period integrals of a holomorphic $3$-form on a rigid Calabi-Yau threefold are interesting from the perspective of number theory. Although the (approximate) values of these integrals would be…

In a previous paper, the author introduced a Z-structure in quantum cohomology defined by the K-theory and the Gamma class and showed that it is compatible with mirror symmetry for toric orbifolds. Applying the quantum Lefschetz principle…

A method for deriving the Schrodinger equation for Lagrangian path integral with scaling of local time is given.

We prove a new (conditional) result towards the subconvexity problem for certain automorphic $L$-functions for $\mathrm{GL}_2 \times \mathrm{GL}_3$. This follows from the computation of new $\mathrm{SL}_2$-period integrals associated with…

The aim of this paper is to study certain multiple series which can be regarded as multiple analogues of Eisenstein series. As a prior research, the second-named author considered double analogues of Eisenstein series and expressed them as…

Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single valued integrals of motion each. All…

Integrable systems with a linear periodic integral for the Lie algebra $\mathrm{e}(3)$ are considered. One investigates singulariries of the Liouville foliation, bifurcation diagram of the momentum mapping, transformations of Liouville…