The Riemann Hypothesis-Millennium Prize Problem
نویسندگان
چکیده
منابع مشابه
Problems of the Millennium: the Riemann Hypothesis
with s = 12 + it , and shows that ξ(t) is an even entire function of t whose zeros have imaginary part between −i/2 and i/2. He further states, sketching the proof, that in the range between 0 and T the function ξ(t) has about (T/2π) log(T/2π)− T/2π zeros. Riemann then continues: “Mann finden nun in der That etwa so wiel reelle Nullstellen innerhalb dieser Grenzen, und es ist sehr wahrscheinlic...
متن کاملProblems of the Millennium : The Riemann Hypothesis ( 2004
The Riemann Hypothesis (RH) is one of the seven millennium prize problems put forth by the Clay Mathematical Institute in 2000. Bombieri’s statement [Bo1] written for that occasion is excellent. My plan here is to expand on some of his comments as well as to discuss some recent developments. RH has attracted further attention of late in view of the fact that three popular books were written abo...
متن کاملA “good” problem equivalent to the Riemann hypothesis
We exhibit a sequence cn such that the convergence of ∑ n≥1 cnz n for |z| < 1 is equivalent to the Riemann Hypothesis. We argue that this particular RH-equivalent problem is “better” than most, or perhaps every, other RH-equivalent problem devised so far, in the sense that (we prove) there is a tremendous gap in behaviors of the cn if the RH is true versus if the RH is false.
متن کاملAn Elementary Problem Equivalent to the Riemann Hypothesis
The problem is: Let Hn = n ∑ j=1 1 j be the n-th harmonic number. Show, for each n ≥ 1, that
متن کاملThe Riemann Hypothesis
Associated to classical semi-simple groups and their maximal parabolics are genuine zeta functions. Naturally related to Riemann’s zeta and governed by symmetries, including that of Weyl, these zetas are expected to satisfy the Riemann hypothesis. For simplicity, G here denotes a classical semi-simple algebraic group defined over the field Q of rationals. With a fixed Borel, as usual, ∆0 stands...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Pure Mathematics
سال: 2016
ISSN: 2160-0368,2160-0384
DOI: 10.4236/apm.2016.612069