Zobrazeno 1 - 10
of 13
pro vyhledávání: '"Jaitra Chattopadhyay"'
Autor:
Jaitra Chattopadhyay, Subha Sarkar
Publikováno v:
The Ramanujan Journal. 59:979-992
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f92c70c0acfb9105844fa173e7194eee
https://doi.org/10.1007/s11139-022-00593-1
https://doi.org/10.1007/s11139-022-00593-1
Autor:
Jaitra Chattopadhyay, Anupam Saikia
Publikováno v:
The Ramanujan Journal.
For a prime number $p \geq 5$, we explicitly construct a family of imaginary quadratic fields $K$ with ideal class groups $Cl_{K}$ having $p$-rank ${\rm{rk}_{p}(Cl_{K})}$ at least $2$. We also quantitatively prove, under the assumption of the $abc$-c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::240e0b77dd3d710e4a74f36857881fed
https://doi.org/10.1007/s11139-022-00667-0
https://doi.org/10.1007/s11139-022-00667-0
Publikováno v:
Archiv der Mathematik. 116:403-409
In a commutative ring R with unity, a unit u is called exceptional if $$u-1$$ is also a unit. For $$R = {\mathbb {Z}}/n{\mathbb {Z}}$$ and for any $$f(X) \in {\mathbb {Z}}[X]$$ , an element $${\overline{u}} \in {\mathbb {Z}}/n{\mathbb {Z}}$$ is calle
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::00f0671c03339810a01e232df5795ca4
https://doi.org/10.1007/s00013-020-01558-w
https://doi.org/10.1007/s00013-020-01558-w
Autor:
Jaitra Chattopadhyay, S. Muthukrishnan
Publikováno v:
Acta Arithmetica. 197:105-110
Let $k \geq 1$ be a cube-free integer with $k \equiv 1 \pmod {9}$ and $\gcd(k, 7\cdot 571)=1$. In this paper, we prove the existence of infinitely many triples of imaginary quadratic fields $\mathbb{Q}(\sqrt{d})$, $\mathbb{Q}(\sqrt{d+1})$ and $\mathb
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::52dcabdbeaebd070f2a2c833bb7fb56c
https://doi.org/10.4064/aa200221-16-6
https://doi.org/10.4064/aa200221-16-6
Autor:
Jaitra Chattopadhyay, Anupam Saikia
Publikováno v:
Research in Number Theory. 8
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1d029a8e3e9805e72182117e95301847
https://doi.org/10.1007/s40993-022-00327-8
https://doi.org/10.1007/s40993-022-00327-8
In 2016, in the work related to Galois representations, Greenberg conjectured the existence of multi-quadratic $p$-rational number fields of degree $2^{t}$ for any odd prime number $p$ and any integer $t \geq 1$. Using the criteria provided by him to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::abcca9270459cb668a6b47e304699d42
Publikováno v:
Archiv der Mathematik. 114:271-283
A unit u in a commutative ring with unity R is called exceptional if $$u-1$$ is also a unit. We introduce the notion of a polynomial version of this (abbreviated as $$f\hbox {-exunits}$$) for any $$f(X) \in \mathbb {Z}[X]$$. We find the number of rep
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3777fa3838aa93b86cc848a249e54e3d
https://doi.org/10.1007/s00013-019-01413-7
https://doi.org/10.1007/s00013-019-01413-7
Autor:
Jaitra Chattopadhyay, S. Muthukrishnan
Publikováno v:
Journal of Number Theory. 204:99-112
H. W. Lenstra \cite{lenstra} introduced the notion of an Euclidean ideal class, which is a generalization of norm-Euclidean ideals in number fields. Later, families of number fields of small degree were obtained with an Euclidean ideal class (for ins
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::76038e1ef024e235401fcbec07b2aa75
https://doi.org/10.1016/j.jnt.2019.03.015
https://doi.org/10.1016/j.jnt.2019.03.015
Publikováno v:
Class Groups of Number Fields and Related Topics ISBN: 9789811515132
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 the i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::55550a0d73281c9f45f7596c1d39fd34
https://doi.org/10.1007/978-981-15-1514-9_9
https://doi.org/10.1007/978-981-15-1514-9_9
Autor:
Anupam Saikia, Jaitra Chattopadhyay
For a square-free integer $t$, Byeon \cite{byeon} proved the existence of infinitely many pairs of quadratic fields $\mathbb{Q}(\sqrt{D})$ and $\mathbb{Q}(\sqrt{tD})$ with $D > 0$ such that the class numbers of all of them are indivisible by $3$. In
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4c9eb969870fbd3b46fd52b0c58fc191