Dirichlet L-functions, it is known as the generalized Riemann hypothesis or generalised Riemann hypothesis (GRH). These two statements will be discussed...

this without using the generalized Riemann hypothesis. In 1917, Hardy and Littlewood showed that the generalized Riemann hypothesis implies a conjecture...

In mathematics, the grand Riemann hypothesis is a generalisation of the Riemann hypothesis and generalized Riemann hypothesis. It states that the nontrivial...

1924, Hardy and Littlewood showed under the assumption of the generalized Riemann hypothesis that the number of even numbers up to X violating the Goldbach...

{\displaystyle e^{e^{14}}\approx 2.5\cdot 10^{522284}} assuming the generalized Riemann hypothesis (GRH) for Dirichlet L-functions. In 2019, Huixi Li gave a version...

{\displaystyle \mathrm {Re} (s)>n-{\tfrac {1}{2}}} . According to the generalized Riemann Hypothesis the zeros of ζX (s) are conjectured to lie inside the critical...

odd). In 1923, Hardy and Littlewood showed that, assuming the generalized Riemann hypothesis, the weak Goldbach then-conjecture is true for all sufficiently...

several important conjectures in mathematics, including the generalized Riemann hypothesis. Born to American parents who lived in Paris, de Branges moved...

of interest because of their connection to problems like the generalized Riemann hypothesis, distribution of prime numbers, etc. The connections with random...

Ludwig Siegel, is a type of potential counterexample to the generalized Riemann hypothesis, on the zeros of Dirichlet L-functions associated to quadratic...

{\displaystyle e^{e^{15.85}}\approx 3.6\cdot 10^{3321634}} assuming the Generalized Riemann hypothesis (GRH) for Dirichlet L-functions. Johnston and Starichkova give...

composite without relying on mathematical conjectures such as the generalized Riemann hypothesis. The proof is also notable for not relying on the field of analysis...

Gartcosh railway station, in Scotland Gbiri-Niragu language Generalized Riemann hypothesis Gonadotropin-releasing hormone Gramm-Rudman-Hollings Balanced...

theorem Riemann–Stieltjes integral Riemann series theorem Riemann sum Riemann–von Mangoldt formula Riemann hypothesis Generalized Riemann hypothesis Grand...

function Generalized Riemann hypothesis Lehmer pair Particular values of the Riemann zeta function Prime zeta function Renormalization Riemann–Siegel theta...

Assuming the truth of the generalized Riemann hypothesis (which Miller, confusingly, calls the "extended Riemann hypothesis"), it is known that the group...

It is conjectured that the Selberg class of series obeys the generalized Riemann hypothesis. The series is named in honor of Peter Gustav Lejeune Dirichlet...

and Lenstra, which they proved only assuming the unproved generalized Riemann hypothesis. The Schnorr–Seysen–Lenstra probabilistic algorithm has been...

conjecture Chinese hypothesis (not a conjecture to start with) Doomsday conjecture Euler's sum of powers conjecture Ganea conjecture Generalized Smith conjecture...

function Beta function Gamma function Riemann zeta function Riemann hypothesis Generalized Riemann hypothesis Elliptic function Half-period ratio Jacobi's...

about the real axis, but not if χ is a complex character. The generalized Riemann hypothesis is the conjecture that all the non-trivial zeros lie on the...

conjecture, assuming certain cases of the generalized Riemann hypothesis. Without the generalized Riemann hypothesis, there is no single value of a for which...

result is already quite useful, being an averaged form of the generalized Riemann hypothesis. It is known that the conjecture fails at the endpoint θ = 1...

and formulated a version of a generalized Riemann hypothesis in this setting, as a positivity statement for a generalized function on a topological group...

conjecture Birch and Swinnerton-Dyer conjecture Riemann hypothesis and the generalized Riemann hypothesis. Selberg class S Explicit formulae for L-functions...

the case of x = y = z. The unproven Riemann hypothesis is a special case of the generalized Riemann hypothesis, in the case that χ(n) = 1 for all n....

including insight into their relationship to automorphic forms and the Riemann hypothesis. The class was defined by Atle Selberg in (Selberg 1992), who preferred...

Littlewood had shown earlier that this result followed from the generalized Riemann hypothesis, and Vinogradov was able to remove this assumption. The full...

number theory. Piltz was arguably the first to formulate a generalized Riemann hypothesis, in 1884. Dozenten-Album der Universität Jena: 1858 bis 1908...

Chebotarev density theorem, which imply that if one assumes the generalized Riemann hypothesis then ( Z / n Z ) ∗ {\displaystyle \left(\mathbb {Z} /n\mathbb...