Sanoli Gun

Research Summary:

Cooper,Hirshhorn and Lewis studied certain relations satisfied by the coefficients of certain products of powers of Euler's product and conjectured similar relations which were proved by Ahlgren (J.Number Theory,2001). Following Ahlgren's method,we prove further identities using the theory of modular forms with complex multiplication.
A power series is called lacunary if the arithmetic density of its non zero elements is zero. Let $ \eta(\tau)$ be the Dedekind $\eta$-function. Serre has determined all the even integers $r$ for which $\eta(\tau)^r$ is lacunary. We intend to do similar classification for multiple $\eta$-products of the form $\eta( \tau)^r \eta(3\tau)^s$ where $r,s$ are integers.

Preprints:

1. On some multiplicative relations arising from lacunarity of Dedekind eta-quotients. (with Prof. B.Ramakrishnan)
2. Multiplicative relations of eta products.  (with Prof. B.Ramakrishnan)

Conference/Workshops Attended:

Attended a workshop on Algebraic Geometry held at H.R.I. , Allahabad.

Other Activities:

Gave a series of four lectures on Algebraic Number Theory in the VSSP school .



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