Browsing by Author "Pallewatta, M."

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Certain sums of Mordell-Tornheim zeta values
(Research Symposium on Pure and Applied Sciences, 2018 Faculty of Science, University of Kelaniya, Sri Lanka, 2018) Pallewatta, M.
The multiple zeta values are real numbers studied by many people in different fields. The sum formulas are considered as one of the most famous relations among multiple zeta values. In our research, we study a slightly different type of sums known as Mordell-Tornheim zeta values. Mordell-Tornheim zeta values can be expressed as a rational linear combination of multiple zeta values. In our research, we prove new sum formulas for Mordell-Tornheim zeta values in the case of depth 2 and 3, expressing the sums as single multiples of Riemann zeta values. Also, we obtain weighted sum formulas for double Mordell-Tornheim zeta values. Moreover, we present a sum formula for the Mordell-Tornheim series of even arguments.
On level two analogue of Arakawa-Kaneko zeta function and poly-cosecant numbers
(4th International Research Symposium on Pure and Applied Sciences, Faculty of Science, University of Kelaniya, Sri Lanka, 2019) Pallewatta, M.
We study the level two generalization of Arakawa-Kaneko zeta function originally studied by T. Arakawa and M. Kaneko. We obtain certain new formulas for the level two analogue of Arakawa-Kaneko zeta function. Also, we study the level two generalization of poly-Bernoulli numbers, which is referred to as the poly-cosecant numbers. We obtain a recurrence and two explicit formulas for poly-cosecant numbers. Moreover, we extend those formulas for multiple versions in a similar manner. The latter part is a part of a joint work with M. Kaneko and H. Tsumura
On sum formulas for Mordell - Tornheim zeta values.
(International Research Symposium on Pure and Applied Sciences, 2017 Faculty of Science, University of Kelaniya, Sri Lanka., 2017) Pallewatta, M.; Kaneko, M.
The multiple zeta values are real numbers which are studied by many people in different fields. The multiple zeta values with depth 1 are the Riemann zeta values. The sum formulas are considered as one of the most famous relations among multiple zeta values. In our research, we study a slightly different type of sums known as Mordell-Tornheim zeta values. Mordell-Tornheim zeta values can be expressed as a rational linear combination of multiple zeta values with same depth and weight. We have obtained new sum formulas for Mordell-Tornheim zeta values in the case of depth 2 and 3, expressing the sums as single multiples of Riemann zeta values. Moreover, we introduce reciprocity relations between the Mordell-Tornheim series of even arguments with depth 3 in terms of double and triple zeta values by using integrals of products of Bernoulli polynomials.