**Talk Announcement: **

Title: Voronoi summation formulas for certain arithmetic functions and related identities and omega bounds on error terms

Speaker: Shashank Chorge (IIT, Gandhinagar)

When: Oct 24, 2024, 5:00 PM- 6:00 PM IST

When: Oct 24, 2024, 5:00 PM- 6:00 PM IST

Abstract:The Voronoi summation formulas for the divisor function and $r_2(n)$ are well-known. Not only do these formulas have interesting structure, but they have also been used to improve the error term in the Dirichlet divisor problem and the Gauss circle problem respectively.

In this work we derive Voronoi summation

formulas for some other functions related to the generalized divisor function-$d^2(n)$ and Liouville Lambda function-$\lambda(n)$ and Mobius function-$\mu(n)$. We also make use of Vinogradov-Korobov zero free region for the Riemann zeta function to obtain the results.

We also derive beautiful analogues of Cohen's identity and the Ramanujan-Guinand formula associated to these functions.

We also derive certain Omega-bounds for the weighted sums of $d^2(n)$, $\lambda(n)$ and $\mu(n)$ assuming the Linear Independence conjecture.

This is a joint work with Atul Dixit.

In this work we derive Voronoi summation

formulas for some other functions related to the generalized divisor function-$d^2(n)$ and Liouville Lambda function-$\lambda(n)$ and Mobius function-$\mu(n)$. We also make use of Vinogradov-Korobov zero free region for the Riemann zeta function to obtain the results.

We also derive beautiful analogues of Cohen's identity and the Ramanujan-Guinand formula associated to these functions.

We also derive certain Omega-bounds for the weighted sums of $d^2(n)$, $\lambda(n)$ and $\mu(n)$ assuming the Linear Independence conjecture.

This is a joint work with Atul Dixit.

Best wishes,

Gaurav Bhatnagar, Atul Dixit and Krishnan Rajkumar (organisers)