Koecher-Maass Series have Infinitely Many Critical Zeros

Dr Manish Kumar Pandey, Assistant Professor, Department of Mathematics, has published a paper titled, “Koecher–Maass series have infinitely many critical zeros” in the journal Bull. London Math. Soc. having an Impact Factor of 2.396.

Abstract

The article studies the zeros of the Koecher-Maass series associated with a Siegel cusp form of degree 2. It is proved that the Koecher-Maass series associated with a Siegel cusp form has infinitely many zeros on the critical line.

Practical implementation

It is well known that zeros of the Riemann zeta function have connections with prime numbers. In a similar fashion, one can state the behaviour of the coefficients of such series at primes. These are results of pure mathematical flavour and their immediate application will take time.

Collaborations

1. 1. Dr Jaban Meher, National Institute of Science Education and Research (NISER), Bhubaneshwar
   2. Dr Karamdeo Shankhadhar, Indian Institutes of Science Education and Research (IISER), Bhopal

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