A Unified Partial and Mock Theta Function

Understand

Unary theta functions have played a significant role in the theory of holomorphic modular forms and modular $L$-functions.

• A partial theta functions is defined analogously, but the sum is over part of the integer lattice.
• Such sums fail to have modular properties.
• We give a construction which unifies these partial theta functions with the mock theta function introduced by Ramanujan.