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Total convergence or general divergence in Small Divisors
We study generic holomorphic families of dynamical systems presenting
problems of small divisors with fixed arithmetic. We prove that we have
convergence for all parameter values or divergence everywhere except for an
exceptional set in the potential theory sense. We illustrate this general
principle in different problems of small divisors
Notes on the Riemann Hypothesis
These notes were written from a series of lectures given in March 2010 at the
Universidad Complutense of Madrid and then in Barcelona for the centennial
anniversary of the Spanish Mathematical Society (RSME). Our aim is to give an
introduction to the Riemann Hypothesis and a panoramic view of the world of
zeta and L-functions. We first review Riemann's foundational article and
discuss the mathematical background of the time and his possible motivations
for making his famous conjecture. We discuss some of the most relevant
developments after Riemann that have contributed to a better understanding of
the conjecture.Comment: 2 sections added, 55 pages, 6 figure
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