Introduction E9F5FC

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黎曼猜想

an essay on the Riemann hyothesis, Alain Connes related to F1

An elementary problem equivalent to the Riemann hypothesis

The Riemann hypothesis over finite fields from Weil to the present day James Milne 2015

John Baez on RH and quasicrystals https://golem.ph.utexas.edu/category/2013/06/quasicrystals_and_the_riemann.html

The Riemann hypothesis in characteristic p, its origin and development Part 2. The first steps by Davenport and Hasse Von Peter Roquette (Heidelberg)

http://sagemath.blogspot.lt/2015/11/writing-prime-numbers-and-riemann.html mazur and stein slides and talk http://wstein.org/rh/

In search of the Riemann zeros: strings, fractal membranes and noncommutative spacetimes

elementary number theory stein

Number theory

• Allen Hatcher. Topology of numbers
• Prime numbers: "Cost function". The "cost" of a number may be thought of as the sum of all of its prime factors. What might this reveal about the primes?
• Number of ways to partition a number into primes.
• Prime numbers introduce (non)determinism in that when a prime divides a product, then it must divide one of the factors.
• Primes are both atoms and gaps. And they elucidate the gap of all numbers with respect to infinity.
• Riemann hypothesis: is the unfolding of the primes "pattern free"? Or are there one or more hidden patterns there? A zero of the Riemann zeta function indicates a pattern. So what is a pattern? And what are the limitations on patterns?
• Terrence Tao: Each prime p wants to have weight ln p. Compare with Zipf's law, Zipf-Mandelbrot law, Yule-Simon distribution, Preferential attachment, Matthew effect, Pareto's principle.
• If there is a zero in the Riemann function's zone, then there is a function that it can't mimic?
• Arithmetic derivative

Riemann Zeta function, Riemann hypothesis

• Zeta function of a graph (related to the Riemann zeta function) discussed by Viennot and related to heaps of pieces (and paths on graphs).
  • http://coursimsc2017.xavierviennot.org/Ch_5.html
  • Zeta function on graphs revisited with the theory of heaps of pieces https://www.imsc.res.in/~viennot/