October 13, 2021

Research Centre Publishes New Paper on Fractional Differential Relations for the LERCH ZETA FUNCTION

AIMS Cameroon’s Research Centre has published a new paper titled: “FRACTIONAL DIFFERENTIAL RELATIONS FOR THE LERCH ZETA FUNCTION”. The co-authors are the Research Chair Dr. Jean Daniel Djida and maths genius Prof. Arran Fernandez of the Eastern Mediterranean University in Northern Cyprus.

The research work was received on April 16th, 2021, revised on July 19th, 2021, accepted on August 7th, 2021, and published in the Springer Journal Archiv der Mathematik.

The Riemann Zeta function is one of the most important functions in the field of Analytic Number Theory. It is the subject of the famous Riemann hypothesis, as well as the Lindelöf hypothesis and several other unsolved mathematical problems. Its properties contain the key to describing the distribution of the prime numbers, which in turn is important in Cryptography and Computer security.

There are many generalizations of the Riemann zeta function, such as the Dirichlet L-functions in number theory, and the Hurwitz and Lerch zeta functions which are again analytic functions of complex variables. In this work, Arran Fernandez and Jean-Daniel Djida focused on the latter functions.

Both mathematicians explored a recently opened approach to the study of Zeta Functions, namely the approach of Fractional Calculus. By utilising the machinery of fractional derivatives and integrals, which have rarely been applied in analytic Number Theory before, they were able to obtain some fractional differential relations and finally a partial differential equation of fractional type which is satisfied by the Lerch Zeta function.

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