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Session S26 - Finite fields and applications

Friday, July 16, 11:00 ~ 11:20 UTC-3

Clausen’s formula and high Picard rank K3 surfaces.

Adriana Salerno

Bates College, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Clausen’s formula is a classical identity characterizing certain hypergeometric series as squares of other hypergeometric series. Evans-Greene and Fuselier-Long-Ramakrishna-Swisher-Tu have described finite field analogues of this identity. Clausen’s formula also arises in the context of Picard-Fuchs equations satisfied by holomorphic forms on geometrically natural one-parameter families of K3 surfaces. We discuss the implications for point counting on such K3 surfaces over finite fields.

Joint work with Ursula Whitcher (Mathematical Reviews, AMS).

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