Theoretical Statistics and Mathematics Unit Monday Colloquium Date: September 24, 2018 Time: 04:15 P.M. Venue: L-infinity, Stat-Math Unit (5th Floor, A.N. Kolmogorov Bhavan) Rupam Barman IIT Guwahati Hypergeometric series in Arithmetic Geometry Abstract In 1987, John Greene introduced the notion of hypergeometric series over finite fields analogous to classical hypergeometric series (Trans. Amer. Math. Soc. 301 (1987)). Finite field hypergeometric series were developed mainly to simplify character sum evaluations. After 10 years, Ken Ono found interesting relations between Greene's finite field hypergeometric series and L-functions of elliptic curves (Trans. Amer. Math. Soc. 350 (1998)). In 2013, Dermot McCarthy extended the finite field hypergeometric series to the p-adic setting (Pacific J. Math. 261 (2013)). In this talk, I will introduce finite field and p-adic hypergeometric series, and show how their values are related to L-functions of elliptic curves. ALL ARE CORDIALLY INVITED
Theoretical Statistics and Mathematics Unit Monday Colloquium Date: September 24, 2018 Time: 04:15 P.M. Venue: L-infinity, Stat-Math Unit (5th Floor, A.N. Kolmogorov Bhavan) Rupam Barman IIT Guwahati Hypergeometric series in Arithmetic Geometry Abstract In 1987, John Greene introduced the notion of hypergeometric series over finite fields analogous to classical hypergeometric series (Trans. Amer. Math. Soc. 301 (1987)). Finite field hypergeometric series were developed mainly to simplify character sum evaluations. After 10 years, Ken Ono found interesting relations between Greene's finite field hypergeometric series and L-functions of elliptic curves (Trans. Amer. Math. Soc. 350 (1998)). In 2013, Dermot McCarthy extended the finite field hypergeometric series to the p-adic setting (Pacific J. Math. 261 (2013)). In this talk, I will introduce finite field and p-adic hypergeometric series, and show how their values are related to L-functions of elliptic curves. ALL ARE CORDIALLY INVITED
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