arXiv subjects

Ramesh Sreekantan

Publications and source records attributed to Ramesh Sreekantan.

21 records · Page 2Linked to original sources

arXiv2003

K1 of products of Drinfeld Modular Curves and Special Values of L-functions

Let $X_0(I)$ be the Drinfeld's modular curve with level $I$ structure, where $I$ is a monic square-free ideal in $\F_{q}[T]$. In this paper we show the existence of an element in the motivic cohomology group $H^3_{\M}(X_0(I) \times X_0(I),\Q(2))$ whose regulator is related to a special value of a Ranking-Selberg convolution $L$-function. This result is the function field analogue of a theorem of Beilinson for the self product of a modular curve.

math.NT↗

arXiv2001

An analogue of cyclotomic units for products of elliptic curves

We construct certain elements in the integral motivic cohomology group $H^3_{\cal M}(E \times E',\Q(2))_{\ZZ}$, where $E$ and $E'$ are elliptic curves over $\Q$. When $E$ is not isogenous to $E'$ these elements are analogous to `cyclotomic units' in real quadratic fields as they come from modular parametrisations of the elliptic curves. We then find an analogue of the class number formula for real quadratic fields. Finally we use the Beilinson conjectures for $E \times E'$ to deduce them for products of $n$ elliptic curves. A certain amount of this paper is expository in nature.

math.NT↗

arXiv2000

Relations among Heegner Cycles on families of abelian surfaces

We compute relations of rational equivalence among special codimensional two cycles on families of abelian surfaces using elements of higher chow groups.

math.AG↗