Shivam Patel

collaborators

2 papers

math.GM2026

Derivative Sums of Balanced Gamma Quotients and Multiple Zeta Values: Five Conjectures of Zhi-Wei Sun

Shivam Nalin Patel

We introduce a uniform reduction for derivative sums of balanced gamma quotients. For exponent data $(a_{i}, e_{i})$ satisfying $\sum_{i} e_{i} a_{i} = 0$ , the translation-dependent gamma prefa…

math.GM2026

Weighted Derivative Sums of a Gamma Quotient: Sun's Conjecture and Cyclotomic Specializations

Shivam Nalin Patel

Let $f (x) = I^ (x)^{2} / (2 I^ (2 x))$ and set $I^»_{I^} \pm = 4 sin^{2} I^\pm$ for $0 < I^\pm < I ¨ /2$ . We establish an elementary parameter identity for a weighted translate of $f$ and derive an explicit f…