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math.NT2017
Zeros of combinations of the Riemann -function and the confluent hypergeometric function on bounded vertical shifts
Atul Dixit, Rahul Kumar, Bibekananda Maji +1
In 1914, Hardy proved that infinitely many non-trivial zeros of the Riemann zeta function lie on the critical line using the transformation formula of the Jacobi theta function. Re…
math.NT2017
Perfect powers in alternating sum of consecutive cubes
Pranabesh Das, Pallab Kanti Dey, B. Maji +1
In this paper, we consider the problem about finding out perfect powers in an alternating sum of consecutive cubes. More precisely, we completely solve the Diophantine equation $(x…