D. S. Ramana

activity

20072017

most citedThe number of rational numbers determined by large sets of integers

11 citations · 14 across the 7 of their papers we have counts for

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7 papers · 1 filter

math.NT2017

On monochromatic representation of sums of squares of primes

Kummari Mallesham, Gyan Prakash, D. S Ramana

When the sequences of squares of primes is coloured with $K$ colours, where $K \geq 1$ is an integer, let $s (K)$ be the smallest integer such that each sufficiently large integer c…

math.NT2017

A Variant of the Truncated Perron's Formula and Primitive Roots

D. S. Ramana, O. Ramaré

We show under the Generalised Riemann Hypothesis that for every $δ > 0$ , almost every prime $q$ in $[Q, 2 Q]$ has the expected of prime primitive roots in the interval $[x,x+x^{\frac{1…

math.NT2009★ 11 cited

The number of rational numbers determined by large sets of integers

Javier Cilleruelo, D. S. Ramana, Olivier Ramare

When $A$ and $B$ are subsets of the integers in $[1, X]$ and $[1, Y]$ respectively, with $∣ A ∣ \geq α X$ and $∣ B ∣ \geq β X$ , we show that the number of rational numbers expressible as $…

math.NT2007

Sum-free subsets of finite abelian groups of type III

R. Balasubramanian, Gyan Prakash, D. S. Ramana

A finite abelian group $G$ of cardinality $n$ is said to be of type III if every prime divisor of $n$ is congruent to 1 modulo 3. We obtain a classification theorem for sum-free su…

math.NT2007

The Large Sieve Inequality for Integer Polynomial Amplitudes

Gyan Prakash, D. S. Ramana

We obtain a close to the best possible version of the large sieve inequality with amplitudes given by the values of a polynomial with integer coefficients of degree $\geq 2$ .

math.NT2007

The Large Sieve Inequality for Quadratic Polynomial Amplitudes

Gyan Prakash, D. S. Ramana

We provide here a modest improvement upon a large sieve inequality for quadratic polynomial amplitudes orginally due to Liangyi Zhao.