Shekhar Suman

collaborators

3 papers

math.GM2025

A note on the Irrationality of $I^¶ (5)$ and Higher Odd Zeta Values

Shekhar Suman

In this note, we prove the irrationality of $I^¶ (5)$ and generalize the method to prove the irrationality of all higher odd zeta values. Our proof relies on the method of contradict…

math.GM2024

An equivalent criteria for irrationality of $I^¶ (5)$

Shekhar Suman

Defining a Beukers [1] like integral for $I^¶ (5)$ as \begin{equation*} I_n:=\int_{(0,1)^5}\frac{(1-x_3)^n(1-x_4)^n P_n(x_1)P_n(x_2)}{1-(1-x_1x_2x_3x_4)x_5} \ dx_1dx_2dx_3dx_4dx_5 \e…

math.GM2024

100% of the zeros of $I^¶ (s)$ are on the critical line

Shekhar Suman

Throughout this manuscript the zeros are counted with multiplicity. We denote by $N (T)$ the number of zeros $I ¨ $ of $I^¶ (s)$ in the critical strip upto height $T$ where $T > 3$ is not…

A note on the Irrationality of I^¶(5) and Higher Odd Zeta Values

An equivalent criteria for irrationality of I^¶(5)

100% of the zeros of I^¶(s) are on the critical line

A note on the Irrationality of $I^¶ (5)$ and Higher Odd Zeta Values

An equivalent criteria for irrationality of $I^¶ (5)$

100% of the zeros of $I^¶ (s)$ are on the critical line