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SEMINAR:Orders of reductions of an elliptic curve in arithmetic progress

Speaker:  Antigona Pajaziti

Title: Orders of reductions of an elliptic curve in arithmetic progressions

Date/Time: 29 December 2021 / 13:40 - 14:30 pm

Hybrid: FENS G035

Zoom Link:https://sabanciuniv.zoom.us/j/94368587993?pwd=WnpVZ3U1MTBBUGFHSTRRT0Flcmlhdz09

Passcode: 658402

Abstract:TLet E be an elliptic curve defined over a number field K with ring of integers R. We consider the set S of all the orders of reductions of E modulo the primes of R. Given an integer m>1, one may ask how many residue classes modulo m have an intersection of positive density with S. Using results of Serre and Katz, we show that there are at least two such residue classes; except for explicit families of elliptic curves and corresponding values of m.  We then describe this exceptional set of elliptic curves and list the values of m when K is of degree at most 3; or K is Galois of degree 4.