23 citations · 51 across the 9 of their papers we have counts for
12 papers
Jacquet--Rallis transfer for GL(2)
Andreas Mihatsch, Siddarth Sankaran, Tonghai Yang
We study archimedean smooth transfer for the Jacquet--Rallis relative trace formula comparison, in particular, identities between orbital integrals on GL(n) and its unitary forms.…
Gaussian test functions and Jacquet-Rallis transfer
Andreas Mihatsch, Siddarth Sankaran, Tonghai Yang
We construct Gaussian test functions for the general linear side of the Jacquet-Rallis relative trace formula comparison. These are functions which are defined in terms of their or…
Zero-dimensional Shimura varieties and central derivatives of Eisenstein series
Siddarth Sankaran
We formulate and prove a version of the arithmetic Siegel-Weil formula for (zero dimensional) Shimura varieties attached to tori, equipped with some additional data. More precisely…
A genus two arithmetic Siegel-Weil formula on X_0(N)
Siddarth Sankaran, Yousheng Shi, Tonghai Yang
We define a family of arithmetic zero cycles in the arithmetic Chow group of a modular curve X_0(N), for N>3 odd and squarefree, and identify the arithmetic degrees of these cycles…
Arithmetic special cycles and Jacobi forms
Siddarth Sankaran
We consider families of special cycles, as introduced by Kudla, on Shimura varieties attached to anisotropic quadratic spaces over totally real fields. By augmenting these cycles w…
Grain boundary diffusion and grain boundary structures of a Ni-Cr-Fe-alloy: Evidences for grain boundary phase transformations
Sai Rajeshwari K, S. Sankaran, K. C. Hari Kumar +4
Grain boundary tracer diffusion of Ni, Fe and Cr was studied in a Ni-base 602CA coarse-grained alloy. A co-existence of several short-circuit contributions was distinguished at hig…
Green forms and the arithmetic Siegel-Weil formula
Luis E. Garcia, Siddarth Sankaran
We construct natural Green forms for special cycles in orthogonal and unitary Shimura varieties, in all codimensions, and, for compact Shimura varieties of type O(p,2) and U(p,1),…
Twisted Hilbert modular surfaces, arithmetic intersections and the Jacquet-Langlands correspondence
Gerard Freixas i Montplet, Siddarth Sankaran
We study arithmetic intersections on twisted (quaternionic) Hilbert modular surfaces and Shimura curves over a real quadratic field. Our first main result is the determination of t…
On two arithmetic theta lifts
Stephan Ehlen, Siddarth Sankaran
Our aim is to clarify the relationship between Kudla's and Bruinier's Green functions attached to special cycles on Shimura varieties of orthogonal and unitary type. These function…
Improper Intersections of Kudla-Rapoport divisors and Eisenstein series
Siddarth Sankaran
We consider a certain family of Kudla-Rapoport cycles on an integral model of a Shimura variety attached to a unitary group of signature (1,1), and prove that the arithmetic degree…
Unitary cycles on Shimura curves and the Shimura lift II
Siddarth Sankaran
We consider two families of arithmetic divisors defined on integral models of Shimura curves. The first was studied by Kudla, Rapoport and Yang, who proved that if one assembles th…
Unitary cycles on Shimura curves and the Shimura lift I
Siddarth Sankaran
This paper concerns two families of divisors, which we call the `orthogonal' and `unitary' special cycles, defined on integral models of Shimura curves. The orthogonal family was s…