Modular forms of weight \frac12 defined on products of 𝑝-adic upper half-planes

Schwartz, Anne

doi:10.1090/S0002-9947-1993-1154543-7

Modular forms of weight $\frac 12$ defined on products of $p$-adic upper half-planes
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Trans. Amer. Math. Soc. 335 (1993), 757-773 Request permission

Abstract:

We continue Stark’s study of modular forms defined on products of $p$-adic upper half-planes. Specifically, we restrict to the case of the number field $\mathbb {Q}$ and one finite prime. In this setting we develop a multiplier system for modular forms of weight $\frac {1} {2}$, and provide an example of such a form.

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Dirichlet series and automorphic forms