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math.NT2026
Positivity and tails of Jacobi theta series
Nian Hong Zhou
Using elementary -series manipulations, we establish a positivity property for the tails of the Jacobi theta series. Specifically, for integers and , define \[…
math.NT2026
Theta functions and transformations of bilateral basic hypergeometric series
Nian Hong Zhou
We establish new transformation formulas involving theta functions and certain bilateral basic hypergeometric series. From these formulas, we construct companion -series for a c…