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Title: THE CENTRAL LIMIT THEOREM IN ALGEBRA AND NUMBER THEORY.

Time: 4-5pm.

Venue: Ramanujan Hall.

Speaker: Prof. M. Ram Murty (Queen's University)

Abstract: The central limit theorem in probability theory expanded its
influence into number theory in the middle of the 20th century. This
began with the celebrated Erdos-Kac theorem which generalized the
classical theorem of Hardy and Ramanujan regarding the "normal" number of
prime divisors of a random integer. Since then, probabilistic number
theory has blossomed into various branches resulting in spectacular
foliage including unexpected applications in algebra. In particular, one
can combine the study of Artin L-series and probabilistic number theory to
derive a central limit theorem for the normal number of prime factors of
Fourier coefficients of modular forms. We will report on this research
along with recent (and not so recent) results obtained in joint work with
V. Kumar Murty,
Arpita Kar and Neha Prabhu.