M. Ram Murty

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20142016

most citedFinite Ramanujan expansions and shifted convolution sums of arithmetical functions

14 citations · 15 across the 3 of their papers we have counts for

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math.NT2025

Brun's inequality for a geometric lattice

M. Ram Murty, Sunil Naik

In a seminal paper of 1915, V. Brun introduced Brun's sieve, which is based on Brun's inequality for the Möbius function and is a very powerful tool in modern number theory. The im…

math.NT2016★ 14 cited

Finite Ramanujan expansions and shifted convolution sums of arithmetical functions

Giovanni Coppola, M. Ram Murty, Biswajyoti Saha

For two arithmetical functions $f$ and $g$ , we study the convolution sum of the form $\sum_{n \leq N} f (n) g (n + h)$ in the context of its asymptotic formula with explicit error terms…

math.NT2015★ 1 cited

On a conjecture of Erdös and certain Dirichlet series

Tapas Chatterjee, M. Ram Murty

Let $f : Z / q Z \to Z$ be such that $f (a) = \pm 1$ for $1 \leq a < q$ , and $f (q) = 0$ . Then Erdös conjectured that $\sum_{n \geq 1} \frac{f ( n )}{n} \neq = 0$ . For $q$ even, this is trivially…

math.NT2014

Non-vanishing of Dirichlet series with periodic coefficients

Tapas Chatterjee, M. Ram Murty

For any periodic function $f : N \to C$ with period $q$ , we study the Dirichlet series $L (s, f) := \sum_{n \geq 1} f (n) / n^{s} .$ It is well-known that this admits an ana…