New large value estimates for Dirichlet polynomials
The paper by Larry Guth and James Maynard introduces enhanced bounds for Dirichlet polynomials, impacting prime number theory and the Riemann zeta function. It offers zero density estimates and primes' behavior in short intervals, aiding prime number distribution comprehension. The 48-page paper falls under Number Theory with MSC classes 11M26 and 11N05, holding substantial implications for number theory.
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The paper titled "New large value estimates for Dirichlet polynomials" by Larry Guth and James Maynard presents improved bounds on the frequency of Dirichlet polynomials taking large values. These estimates are crucial in analytic number theory concerning prime numbers and the Riemann zeta function. The research results in a zero density estimate and provides asymptotic behavior for primes in short intervals. The findings contribute to understanding the distribution of prime numbers and related functions. The paper is 48 pages long and falls under the subject of Number Theory with MSC classes 11M26 and 11N05. The implications of the new estimates have significant implications for various aspects of number theory.
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