## Quotients de Fermat et nombres premiers généralisés de Wieferich

Jeudi 14 novembre 2019, 11:30 à 12:30

Salle de séminaires du LMRS

Igor SHPARLINSKI

(University of New South Wales, Australia)

Abstract. We present some background and also recent advances due to J. Bourgain, K. Ford, S. Konyagin and the speaker.
These new results are based on a combination of various techniques including the distribution of smooth numbers, distribution of elements of multiplicative subgroups of residue rings, bound of Heilbronn exponential sums and a large sieve inequality with square moduli. These techniques will be briefly explained as well.