arXiv subjects

Kotyada Srinivas

Publications and source records attributed to Kotyada Srinivas.

6 recordsLinked to original sources

arXiv2025

Behaviour of Newton Polygon over polynomial composition

In this paper, we study the structure of Newton polygons for compositions of polynomials over the rationals. We establish sufficient conditions under which the successive vertices of the Newton polygon of the composition $ g(f^n(x)) $ with respect to a prime $ p $ can be explicitly described in terms of the Newton polygon of the polynomial $ g(x) $. Our results provide deeper insights into how the Newton polygon of a polynomial evolves under iteration and composition, with applications to the study of dynamical irreducibility, eventual stability, non-monogenity of tower of number fields, etc.

math.NT↗

arXiv2021

On the Diophantine equation $cx^2+p^{2m}=4y^n$

Let $c$ be a square-free positive integer and $p$ a prime satisfying $p\nmid c$. Let $h(-c)$ denote the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{-c})$. In this paper, we consider the Diophantine equation $$cx^2+p^{2m}=4y^n,~~x,y\geq 1, m\geq 0, n\geq 3, \gcd(x,y)=1, \gcd(n,2h(-c))=1,$$ and we describe all its integer solutions. Our main tool here is the prominent result of Bilu, Hanrot and Voutier on existence of primitive divisors in Lehmer sequences.

math.NT↗

arXiv2011

On the zeros of functions in the Selberg class

It is proved that under some suitable conditions, the degree two functions in the Selberg class have infinitely many zeros on the critical line.

math.NT↗

arXiv2011

On the zeros of the Epstein zeta function

In this article, we count the number of consecutive zeros of the Epstein zeta-function, associated to a certain quadratic form, on the critical line with ordinates lying in $[0,T], T$ sufficiently large and which are separated apart by a given positive number $V$.

math.NT↗

arXiv2008

Counting squarefree discriminants of trinomials under abc

For an odd positive integer $n\ge 5$, assuming the truth of the $abc$ conjecture, we show that for a positive proportion of pairs $(a,b)$ of integers the trinomials of the form $t^n+at+b (a,b\in \mathbb Z)$ are irreducible and their discriminants are squarefree.

math.NT↗

arXiv2008

On the Oppenheim's "factorisatio numerorum" function

Let $f(n)$ denote the number of distinct unordered factorisations of the natural number $n$ into factors larger than 1.In this paper, we address some aspects of the function $f(n)$.

math.NT↗