A5042903859- Algebraic Geometry and Number Theory
- Analytic Number Theory Research
- Advanced Topology and Set Theory
- Mathematical Dynamics and Fractals
- Limits and Structures in Graph Theory
- Rings, Modules, and Algebras
- History and Theory of Mathematics
- Geometric and Algebraic Topology
- Meromorphic and Entire Functions
- Advanced Algebra and Geometry
- Commutative Algebra and Its Applications
- Polynomial and algebraic computation
- History and advancements in chemistry
- Graph theory and applications
Indian Institute of Science Education and Research Thiruvananthapuram
2024
Indian Statistical Institute
2023
Chennai Mathematical Institute
2022
Institute of Mathematical Sciences
2019
Gerth generalised Cohen-Lenstra heuristics to the prime $p=2$. He conjectured that for any positive integer $m$, limit $$ \lim_{x \to \infty} \frac{\sum_{0 < D \le X, \atop{ \text{squarefree} }} |{\rm Cl}^2_{\Q(\sqrt{D})}/{\rm Cl}^4_{\Q(\sqrt{D})}|^m}{\sum_{0 1} exists and proposed a value limit. Gerth's conjecture was proved by Fouvry Kluners in 2007. In this paper, we generalize their result obtaining lower bounds average of $|{\rm Cl}^2_{\L}/{\rm Cl}^4_{\L}|^m$, where $\L$ varies over an...
Lenstra introduced the notion of Euclidean ideal classes for number fields to study cyclicity their class groups. In particular, he showed that group a field with unit rank greater than or equal one is cyclic if and only it has class. The part in above result conditional on extended Riemann hypothesis. Graves Murty does not require hypothesis four its Hilbert abelian over rationals. this article, we real cubic quadratic groups show they have under certain conditions.
Let $\mathbf{K}$ be a number field and $\mathfrak{q}$ an integral ideal in $\mathcal{O}_{\mathbf{K}}$. A result of Tatuzawa from 1973, computes the asymptotic (with error term) for ideals with norm at most $x$ class narrow ray group modulo $\mathfrak{q}$. This bounds term constant whose dependence on is explicit but not explicit. The aim this paper to prove fully bound term.
For any non-integral positive real number c, sequence (⌊n c ⌋) n is called a Pjateckii-Šapiro sequence. Given in the interval 1 , 12 11, it known that of primes this up to x has an asymptotic formula. We would like use techniques Gupta and Murty study Artin's problems for such primes. will prove even though set density zero fixed one can show there exist natural numbers which are primitive roots infinitely many 77 7 - 4.