N. Saradha

activity

20112025

collaborators

7 papers

math.NT2025

Explicit and Mixed Estimates for Thue inequalities with few coefficients

N. Saradha, Divyum Sharma

Let $F (x, y)$ be an irreducible form of degree $r \geq 3$ and having $s + 1$ non-zero coefficients. Let $h \geq 1$ be an integer and consider the Thue inequality $∣ F (x, y) ∣ \leq h .$ Fol…

math.NT2022

Diagonalizable Thue Equations -- revisited

N. Saradha, Divyum Sharma

Let $r, h \in N$ with $r \geq 7$ and let $F (x, y) \in Z [x, y]$ be a binary form such that \[ F(x , y) =(αx + βy)^r -(γx + δy)^r, \] where $α$ , $β$ , $γ$ and $δ$ are alge…

math.NT2021

Rational solutions to the Variants of Erdős- Selfridge superelliptic curves

Pranabesh Das, Shanta Laishram, N. Saradha +1

For the superelliptic curves of the form $(x + 1) \dots (x + i - 1) (x + i + 1) \dots (x + k) = y^{ℓ}$ with $x, y \in Q$ , $y \neq = 0$ , $k \geq 3$ , $1 \leq i \leq k$ , $ℓ \geq 2,$ a prim…

math.NT2017

On interlacing of zeros of certain family of modular forms

Ekata Saha, N. Saradha

Let $k = 12 m (k) + s \geq 12$ for $s \in {0, 4, 6, 8, 10, 14}$ , be an even integer and $f$ be a normalised modular form of weight $k$ with real Fourier coefficients, written as $$ f=E_k+\su…

math.NT2016

Contributions to a conjecture of Mueller and Schmidt on Thue inequalities

N. Saradha, Divyum Sharma

Let $F (X, Y) = i = 0 \sum s a_{i} X^{r_{i}} Y^{r - r_{i}} \in Z [X, Y]$ be a form of degree $r = r_{s} \geq 3$ , irreducible over $Q$ and having at most $s + 1$ non-zero coefficient…

math.NT2016

Thue's inequalities and the hypergeometric method

Shabnam Akhtari, N. Saradha, Divyum Sharma

Following a method originally due to Siegel, we establish upper bounds for the number of primitive integer solutions to inequalities of the shape $0 < ∣ F (x, y) ∣ \leq h$ , where $F(x ,…

math.NT2011

On a conjecture of Pomerance

L. Hajdu, N. Saradha, R. Tijdeman

We say that k is a P-integer if the first phi(k) primes coprime to k form a reduced residue system modulo k. In 1980 Pomerance proved the finiteness of the set of P-integers and co…