On the zeros of the Riemann Zeta function

By L. Fekih-Ahmed. 2010

124 citations recorded by the source corpus.

This paper is divided into two independent parts. The first part presents new integral and series representations of the Riemaan zeta function. An equivalent formulation of the Riemann hypothesis is given and few results on this formulation are briefly outlined. The second part exposes a totally different approach. Using the new series representation of the zeta function of the first part, exact information on its zeros is provided.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/84f2cd8b87482321da32162ca260cc0d80032f73

How researchers see this paper

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In Algebra and Number Theory

1. Emanuel Carneiro
2. Vorrapan Chandee
3. T. Trudgian
4. Michael J. Mossinghoff
5. Alexandra Florea
6. Dave Platt

In Mathematical Physics

1. Emanuel Carneiro
2. Vorrapan Chandee
3. Michael J. Mossinghoff
4. T. Trudgian
5. Shuanglin Shao
6. Aynur Bulut
7. William Beckner

Citations in the corpus

• Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function (2014, background): “Stechkin [18] improved this in 1970, showing that one may select”
• On the Hurwitz Zeta Function (2011, methodology): “−1)ζ(s,a) = X∞ n=1 Sn(s,a) 1 n+ 1 + a− 1 n . Proof The proof the first statement follows the same steps as in [6] for example. As for the second statement, we can either proceed as in [5] or as in [3]1. In [3], the proof was given for ζ(s) (i.e. a= 1) and uses an estimate of the exact asymptotic or”
• Bounding ζ(s) in the critical strip (2010, background): “Introduction Littlewood showed in 1924 (see [8]) that the Riemann Hypothesis (RH) implies a strong form of the Lindelöf Hypothesis, namely, on RH, for large real numbers t there is a constant C such that ∣ζ ( 1 2 + it ∣≪ exp ( C log t log log t ) .”