## Sporadic sequences, modular forms and new series for $$1/\pi$$.(English)Zbl 1336.11031

Summary: Two new sequences, which are analogues of six sporadic examples of D. Zagier, are presented. The connection with modular forms is established and some new series for $$1/\pi$$ are deduced. The experimental procedure that led to the discovery of these results is recounted. Proofs of the main identities will be given, and some congruence properties that appear to be satisfied by the sequences will be stated as conjectures.

### MSC:

 11F11 Holomorphic modular forms of integral weight 11F27 Theta series; Weil representation; theta correspondences 11Y60 Evaluation of number-theoretic constants

### Keywords:

congruence; modular form; pi; sporadic sequence
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### References:

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