Journal of the Ramanujan Mathematical Society
Volume 41, Issue 3, September 2026 pp. 277–285.
Exponential sums weighted by divisor functions and its applications
Authors:
Nilanjan Bag and Dwaipayan Mazumder
Author institution:Department of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab 147 004, India.
Summary:
Take a real polynomial f with irrational leading co-efficient. This short
article is devoted to the study of weighted exponential sums, when weighted
by divisor functions. In particular we are interested in studying the sum
of the form ∑ {n ≤ N} τ (n)e(f(n)), for some polynomial f,
where τ is the divisor function and µ is the M öbius function.
We get non-trivial estimates when the leading co-efficient α of f
belongs to the ‘‘minor arc’’.
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