17 research outputs found
Hybrid moments of the Riemann zeta-function
The "hybrid" moments
of the Riemann zeta-function on the critical line are
studied. The expected upper bound for the above expression is
. This is shown to be true for certain specific
values of the natural numbers , and the explicitly determined range
of . The application to a mean square bound for the Mellin
transform function of is given.Comment: 27 page
Primality testing and Abelian varieties over finite fields
From Gauss to G|del, mathematicians have sought an efficient algorithm to distinguish prime numbers from composite numbers. This book presents a random polynomial time algorithm for the problem. The methods used are from arithmetic algebraic geometry, algebraic number theory and analyticnumber theory. In particular, the theory of two dimensional Abelian varieties over finite fields is developed. The book will be of interest to both researchers and graduate students in number theory and theoretical computer science