In this paper, we define the Schrödinger-Weil representation for the Jacobi group and construct covariant maps for the Schrödinger-Weil representation. Using these covariant maps, we construct Jacobi forms with respect to an arithmetic subgroup of the Jacobi group.

We construct a Petersson-Weil type Kähler form on the moduli spaces of Higgs bundles over a compact Kähler manifold. A fiber integral formula for this form is proved, from which it follows that the Petersson-Weil form is the curvature of a certain determinant line bundle, equipped with a Quillen metric, on the moduli space of Higgs bundles over a projective manifold. The curvature of the Peters...

Weil-Felix reaction with blood of patients suffering ̂ from scrub typhus during its course shows significant agglutination titres against yproteus XK strains. In Bombay. Patel (1940) reported on two cases but the titres were ^r below the diagnostic level. Later, two more cases clinically suspected and serologically confirmed were reported by Patel (1943) and Patel (1943). Systematic Weil-Felix r...

BACKGROUND Though rickettsiosis is common in India, there is paucity of rickettsial retinitis (RR) reports from India. Moreover, rickettsial sub-types and their association with retinitis have not been studied. We are reporting a case series of presumed RR with their course of the disease, visual outcome, and association with rickettsial sub-type based on Weil-Felix test. FINDINGS This is a r...

In India the presence of Rickettsial disease in human is documented in many states however, the data on presence of Rickettsial infection in Andhra Pradesh is very scare. Therefore, a study was undertaken in Chittoor district (A.P.) to see the prevalence of Rickettsial infection in human and rodent population. 3-5 ml of human blood samples were collected from the patients attending the nearest ...

In this paper we study the systole function along WeilPetersson geodesics. We show that the square root of the systole function is uniform Lipschitz on the Teichmüller space endowed with the Weil-Petersson metric. The inradius of a metric space is the largest radius of metric balls contained in the interior of the metric space. As applications of the result above, we study the growth of the Wei...

For an elliptic curve E over any field K, the Weil pairing en is a bilinear map on n-torsion. For K of characteristic p > 0, the map en is degenerate if and only if n is divisible by p. In this paper, we consider E over the dual numbers K[ǫ] and define a non-degenerate “Weil pairing on ptorsion” which shares many of the same properties of the Weil pairing. We also show that the discrete logarit...

In this paper, we continue our study of the Weil-Petersson geometry as in the previous paper [10], in which we have proved the boundedness of the Weil-Petersson volume, among the other results. The main results of this paper are that the volume and the integrations of Ricci curvature of the Weil-Petersson metric on the moduli space are rational numbers. In particular, the Ricci curvature define...

In this paper, we continue our study of the Weil-Petersson geometry as in the previous paper [10], in which we have proved the boundedness of the Weil-Petersson volume, among the other results. The main results of this paper are that the volume and the integrations of Ricci curvature of the Weil-Petersson metric on the moduli space are rational numbers. In particular, the Ricci curvature define...