# Improved eigenvalue bounds for Schr\"odinger operators with slowly decaying potentials

## TL;DR

This paper extends eigenvalue bounds for Schrödinger operators with slowly decaying potentials to higher dimensions and discusses related examples concerning the Laptev--Safronov conjecture.

## Contribution

It generalizes previous results to higher dimensions and explores implications for the Laptev--Safronov conjecture.

## Key findings

- Eigenvalue bounds are extended to higher dimensions.
- Examples related to the Laptev--Safronov conjecture are discussed.
- The work provides new insights into the spectral properties of Schrödinger operators.

## Abstract

We extend a result of Davies and Nath on the location of eigenvalues of Schr\"odinger operators with slowly decaying complex-valued potentials to higher dimensions. In this context, we also discuss various examples related to the Laptev--Safronov conjecture.