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On the irreducible factors of a polynomial II
Anuj Jakhar, Srinivas Koytada
We give a lower bound for the degree of an irreducible factor of a given polynomial. This improves and generalizes the results obtained in [4, On the irreducible factors of a polyn…
Some remarks related to Maeda's conjecture
M. Ram Murty, K. Srinivas
In this article we deal with the problem of counting the number of pairs of normalized eigenforms of weight and level such that where $a_p (…
On the zeros of the Epstein zeta function
Anirban Mukhopadhyay, Krishnan Rajkumar, Kotyada Srinivas
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],…
Counting squarefree discriminants of trinomials under abc
Anirban Mukhopadhyay, M. Ram Murty, Kotyada Srinivas
For an odd positive integer , assuming the truth of the conjecture, we show that for a positive proportion of pairs of integers the trinomials of the form $t^…
On the Oppenheim's "factorisatio numerorum" function
Florian Luca, Anirban Mukhopadhyay, Kotyada Srinivas
Let denote the number of distinct unordered factorisations of the natural number into factors larger than 1.In this paper, we address some aspects of the function …
On the zeros of functions in the Selberg class
Anirban Mukhopadhyay, Kotyada Srinivas, Krishnan Rajkumar
It is proved that under some suitable conditions, the degree two functions in the Selberg class have infinitely many zeros on the critical line.