arXiv subjects

Priya Dhankhar

Publications and source records attributed to Priya Dhankhar.

2 recordsLinked to original sources

arXiv2026

Gauss sum with principal multiplicative character

Let $R$ be a finite ring with unity, $ψ: R \to \mathbb{C}^\times$ be an additive character of $R$, and $ χ_0 $ be the principal multiplicative character ($i.e.$, $χ_0(x) = 1 \quad \text{for all } x \in R^\times$), then the Gauss sum is \[ G(χ_0, ψ) = \sum_{x \in R^\times} ψ(x). \] In this paper, we give an explicit formula for a more general form of the Gauss sum $G(χ_0, ψ)$. Interestingly, the formula extends the known formula of classical Ramanujan's sum to the context of finite rings. As an application, we derive the eigenvalues for a more general form of the unitary Cayley graph $\text{Cay}(R, R^{\times})$ using the formula.

math.CO↗

arXiv2026

Nonexistence results of generalized bent functions from $\mathbb{Z}_3^n$ to $ \mathbb{Z}_m$

In this paper, we investigate generalized bent functions (GBFs) from $\mathbb{Z}_3^n$ to $\mathbb{Z}_m$. We show that GBFs exist whenever $3$ divides $m$, while several nonexistence results are obtained when $3\nmid m$. In particular, we prove that no GBFs exist for $n=1,2$ when $m$ is odd and not divisible by $3$. For the case $n=3$, we establish the nonexistence of GBFs $f:\mathbb{Z}_3^3 \rightarrow \mathbb{Z}_{5\cdot11^r}$ for all nonnegative integers $r$. Finally, we show that no GBF exists from $\mathbb{Z}_3$ to $\mathbb{Z}_{2m'}$ and $\mathbb{Z}_3^2$ to $\mathbb{Z}_{2m'}$, where $m'$ is odd and not divisible by $3$.

math.CO↗