Zeros of $p$-adic hypergeometric series

Abstract: Let $p$ be an odd prime. McCarthy initiated a study of hypergeometric functions in the $p$-adic setting. This function can be understood as $p$-adic analogue of Gauss' hypergeometric function, and some kind of generalisation of Greene's hypergeometric function over finite fields. In this talk we investigate arithmetic properties of certain families of McCarthy's hypergeometric functions. In particular, we explicitly discuss all the possible values of these functions. Moreover, we discuss zeros of these functions.

number theory

Audience: researchers in the discipline

POINT: New Developments in Number Theory

Series comments: There will be two 20-minute contributed talks during each meeting aimed at a general number theory audience, including graduate students.

Participants are welcome to stay following the talks to have further discussions with the speakers or meet other audience members.

To join our mailing list for talk reminders and other updates, send an email to NDNTseminar+join[AT ]g-groups[DOT]wisc[DOT]edu. Note: You will receive an automatic response prompting you to either click on a button, or to reply to that automatic email. Please use the latter option.