# Square-free integers represented by binary quadratic forms of a fixed discriminant (online broadcast in lecture hall)

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Speaker:

Lalit Vaishya
Affiliation:

The Institute of Mathematical Sciences Chennai India
Date:

Tue, 12/09/2023 - 11:30 - 11:50
Location:

MPIM Lecture Hall
Parent event:

Conference for Young Number Theorists in Bonn In this Work, we prove a result concerning the infinitude of square-free integers represented by a class of polynomials in two variables. More precisely, we prove that infinitely many square-free positive integers are represented by a primitive integral positive-definite binary quadratic form of a given discriminant $D$. We obtain our result by deriving an asymptotic formula for the summatory function associated to it using some known analytic properties of $L$-functions. This is a joint work with Manish Kumar Pandey.

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