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Roger Heath-brown




He is known for many striking results. These include an approximate solution to the Artin Conjecture On Primitive Roots , to the effect that out of 3, 5, 7 (or any three similar multiplicatively-independent Square-free Integer s), one at least is a Primitive Root Modulo P , for infinitely many prime numbers ''p''.

In collaboration with S. J. Patterson , he in 1978 proved the Kummer Conjecture On Cubic Gauss Sums , in its Equidistribution Form .

He has applied Burgess's Method on Character Sum s to the Ranks Of Elliptic Curves in families.


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