Titlebook: Exploring the Riemann Zeta Function; 190 years from Riema Hugh Montgomery,Ashkan Nikeghbali,Michael Th. Rass Book 2017 Springer Internation

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Explorations in the Theory of Partition Zeta Functions,case of the multiplicative theory, we provide specialization formulas and results on the analytic continuations of these “partition zeta functions,” find unusual formulas for the Riemann zeta function, prove identities for multiple zeta values, and see that some of the formulas allow for .-adic inte

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Reading Riemann,wareness of the developments in mathematics, and, in particular, in mathematical physics at that time shows that Riemann was working in a very specific environment and that his thinking reflects this environment. It is therefore helpful to know something of this background. Riemann’s short paper on

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,Arthur’s Truncated Eisenstein Series for ,(2, ,) and the Riemann Zeta Function: A Survey,nglands and Arthur. In this survey we focus on the deep connections between Eisenstein series for .(2, .), truncation, and the Riemann zeta function. Applications to zero free regions for the Riemann zeta function and automorphic L-functions are elucidated.

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Some Analogues of Pair Correlation of Zeta Zeros, two Dirichlet .-functions. In each case the relevant Riemann Hypothesis is assumed for obtaining the results. Several auxiliary results necessary for the calculations may be useful in problems about the zeta-function.