Mathematical Sciences: Multiplicative and Additive Theory ofPrime Numbers and Related Topics in Analytic Number Theory
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This research concerns prime number theory, which can be                   divided into two approaches, the multiplicative and the additive.               The multiplicative theory is largely concerned with the duality                 between primes and zeros of the Riemann zeta function.  The                     additive theory is based on exponential sums of primes and                      typically uses characters and Dirichlet L-functions in order to                 express additive characters as sums of multiplicative functions.                The overlap between these two areas is what is being studied in                 this research.  Some specific topics to be examined are pair                    correlation of zeros of zeta functions, prime pairs and their                   connection with Kloostermann sums and Barban-Davenpoort type                    theorems, small gaps between zeta zeros, the function S(T) and                  Siegal zeros.                                                                        This research concerns prime number theory, that is, the                   distribution of the prime numbers in the integers.  Certain                     complex analytic functions, called zeta functions, contain this                 information and so they are studied uses tools from analysis.                   Thus this subject is a nice blending of number theory and                       analysis.  The results are very deep and difficult to come by.                  Goldston has been remarkably successful in solving problems in                  this area.  This research will certainly push forward our                       knowledge substantially in this important area on mathematics.
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{'Code': '126400', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
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