Director of Research (if dissertation) or Advisor (if thesis)
Reznick, Bruce
Zaharescu, Alexandru
Doctoral Committee Chair(s)
Berndt, Bruce C
Committee Member(s)
Nath, Kunjakanan
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
number theory
Frobenius problem
Stern sequence
Farey sequences
Dirichlet L-function
Riemann zeta function
Abstract
In Part I of this thesis, we show that for relatively prime positive integers a,b, there is a maximum integer g(a,b) which is not expressible as ax+by for x,y non-negative, relatively prime integers. We then explore the connections between this quantity and the Frobenius problem, Farey sequence, and Stern sequence. In Part II, we consider the zeros of a polynomial in derivatives of a Dirichlet L-function and give an asymptotic formula for the number of zeros with imaginary part between 1 and large T.
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