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pro vyhledávání: '"Sarkar, Subha"'
Autor:
Molla, Esrafil Ali, Sarkar, Subha
Let $\mathbb{A}=\mathbb{F}_q[T]$ be the polynomial ring over the finite field $\mathbb{F}_q$. In this article, we prove a generalization of T\'oth identity on $\mathbb{A}$ involving arithmetical functions, multiplicative and additive characters.
Externí odkaz:
http://arxiv.org/abs/2206.03184
Autor:
Sarkar, Subha
Let $G$ be a finite abelian group of exponent $n$ and let $A$ be a non-empty subset of $[1,n-1]$. The Davenport constant of $G$ with weight $A$, denoted by $D_A(G)$, is defined to be the least positive integer $\ell$ such that any sequence over $G$ o
Externí odkaz:
http://arxiv.org/abs/2202.00461
Autor:
Sarkar, Subha
The $k$-dimensional generalized Euler function $\varphi_k(n)$ is defined to be the number of ordered $k$-tuples $(a_1,a_2,\ldots, a_k) \in \mathbb{N}^k$ with $1\leq a_1,a_2,\ldots, a_k \leq n$ such that both the product $a_1a_2\cdots a_k$ and the sum
Externí odkaz:
http://arxiv.org/abs/2106.13983
Autor:
Chattopadhyay, Jaitra, Sarkar, Subha
For every positive integer $n$, Sita Ramaiah's identity states that \medskip \begin{equation*} \sum_{a_1, a_2, a_1+a_2 \in (\mathbb{Z}/n\mathbb{Z})^*} \gcd(a_1+a_2-1,n) = \phi_2(n)\sigma_0(n) \; \text{ where } \; \phi_2(n)= \sum_{a_1, a_2, a_1+a_2 \i
Externí odkaz:
http://arxiv.org/abs/2011.10980
Let $p$ be an odd prime number. In this article, we study the number of quadratic residues and non-residues modulo $p$ which are multiples of $2$ or $3$ or $4$ and lying in the interval $[1, p-1]$, by applying the Dirichlet's class number formula for
Externí odkaz:
http://arxiv.org/abs/1810.00227
Let $q\geq 1$ be any integer and let $ \epsilon \in [\frac{1}{11}, \frac{1}{2})$ be a given real number. In this short note, we prove that for all primes $p$ satisfying $$ p\equiv 1\pmod{q}, \quad \log\log p > \frac{\log 6.83}{\frac{1}{2}-\epsilon} \
Externí odkaz:
http://arxiv.org/abs/1809.04827
Autor:
Roy, Bidisha, Sarkar, Subha
Let $r$, $m$ and $k\geq 2$ be positive integers such that $r\mid k$ and let $v \in \left[ 0,\lfloor \frac{k-1}{2r} \rfloor \right]$ be any integer. For any integer $\ell \in [1, k]$ and $\epsilon \in \{0,1\}$, we let $\mathcal{E}_{v}^{(\ell, \epsilon
Externí odkaz:
http://arxiv.org/abs/1808.08725
In this article, we prove some subsets of the set of natural numbers $\mathbb{N}$ and any non-zero ideals of an order of imaginary quadratic fields are fractionally dense in $\mathbb{R}_{>0}$ and $\mathbb{C}$ respectively.
Comment: To appear in
Comment: To appear in
Externí odkaz:
http://arxiv.org/abs/1804.08068
Consider the equation $\mathcal{E}: x_1+ \cdots+x_{k-1} =x_{k}$ and let $k$ and $r$ be positive integers such that $r\mid k$. The number $S_{\mathfrak{z},2}(k;r)$ is defined to be the least positive integer $t$ such that for any 2-coloring $\chi: [1,
Externí odkaz:
http://arxiv.org/abs/1803.00861
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