6 papers
Tadpole Nahm sum as a Wronskian
Shane Chern, Chanh Tran, Tanay Wakhare
We show that the tadpole Nahm sum is essentially a specialization of a series studied by Bartlett and Warnaar. This overlooked connection was first discovered by the internal model…
On conjectural fermionic formulas for the Macdonald index in Argyres-Douglas theories
Shane Chern, Chanh Tran, Tanay Wakhare
We prove a fermionic-bosonic duality relation for the Macdonald index in Argyres-Douglas theories of type , thereby yielding a conjectural fermionic formula due to…
A divisor generating -series and cumulants arising from random graphs
Archit Agarwal, Subhash Chand Bhoria, Pramod Eyyunni +2
Uchimura, in 1987, introduced a probability generating function for a random variable and using properties of this function he discovered an interesting -series identity. He…
Romik's Conjecture for the Jacobi Theta Function
Tanay Wakhare
Dan Romik recently considered the Taylor coefficients of the Jacobi theta function around the complex multiplication point . He then conjectured that the Taylor coefficients $d(…
Iterated Entropy Derivatives and Binary Entropy Inequalities
Tanay Wakhare
We embark on a systematic study of the -th derivative of , where is the binary entropy and are integers. Our motiv…
Prompts have evil twins
Rimon Melamed, Lucas H. McCabe, Tanay Wakhare +3
We discover that many natural-language prompts can be replaced by corresponding prompts that are unintelligible to humans but that provably elicit similar behavior in language mode…