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Topics in Multiplicative Number Theory


We investigate several topics in multiplicative number theory on the distributions of the k-fold divisor function in arithmetic progressions, divisor sums, and gaps between zeros of L-functions. Applications of these topics to the distribution of prime numbers, zeros of the derivative of the Riemann zeta function near the critical line, the generalized de Bruijn-Newman constant, and connections to moments of L-functions and random matrix theory are also discussed.

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