The Modularity of Z.-W. Sun's Conjectural Formulas for $\frac{1}π$

In this work, we establish modular parameterizations for two general formulas for $\frac{1}{π}$ that subsume conjectural Ramanujan type formulas due to Z.-W. Sun, which have remained open since 2011. As an application of this, in a conceptual way we interpret how Sun’s conjectural formulas arise and can be verified, as well as recover other cases that were proved by Cooper, Wan and Zudilin.

The Modularity of Z.-W. Sun's Conjectural Formulas for $\frac{1}{π}$

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The Modularity of Z.-W. Sun's Conjectural Formulas for $\frac{1}{π}$

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The Modularity of Z.-W. Sun's Conjectural Formulas for 1ππ1​

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The Modularity of Z.-W. Sun's Conjectural Formulas for 1ππ1​

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The Modularity of Z.-W. Sun's Conjectural Formulas for $\frac{1}{π}$

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The Modularity of Z.-W. Sun's Conjectural Formulas for $\frac{1}{π}$

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