Revision #649 → #1538 · back to history
addedRiemann hypothesis09dcf6eb9b6b
addedTrivial zeros of zeta91e22063c566
addedNontrivial zeros of zeta82057fbbc8c5
addedCritical line982d426c53c0
addedRiemann zeta function (Dirichlet series)d8296e3842d5
addedEuler product formula9907377eb347
addedZeta–eta relation252a58ab6e9f
addedFunctional equation of zeta1e3e6a8ba41b
addedTrivial zeros at negative even integers90dd9adfc18a
addedValue zeta(0) = -1/297ced37deee5
addedRiemann's prime/prime-power counting functiona4bdf27b72a3
addedRecovering primes via Möbius inversion69566f63a68d
addedRiemann's explicit formula617bc1b4eda2
addedLogarithmic integral function (Cauchy principal value)dd281d693365
addedvon Koch's prime number theorem error bound under RH5d2502cb8e56
addedSchoenfeld's bound on Chebyshev's psi under RHf341658209f6
addedDudek's explicit Cramér-type prime gap under RH74f835363320
addedMöbius Dirichlet series equivalence to RH03b7f0a46d6d
addedMertens function41d2575d1ccc
addedLittlewood's Mertens-function bound equivalent to RH8eab55123027
addedSoundararajan's conditional bound on M(x)72cd649967f1
addedDisproof of the Mertens conjecture29711b48919c
addedBjörner's Euler-characteristic equivalence99ed916a4dfa
addedRobin's theorem2b0c08ec9bd5
addedLagarias's harmonic-number criterion8148aaad8ba7
addedTotient/primorial inequality equivalent to RHf88a73ad2c60
addedFranel–Landau Farey sequence equivalence2f9e88cf59af
addedMassias–Nicolas–Robin bound on Landau's g(n)d55da8c3f7f1
addedLindelöf hypothesis7ed665a4cd6b
addedRH bounds for growth of zeta in the critical strip8bde5ea271ca
addedCramér's prime gap bound under RH465888609085
addedRiesz criterionf99ce037441b
addedNyman's density criterion6e18a961d544
addedBeurling extension of Nyman's criterion0368a2483091
addedSalem's integral equation criterion9714f67cacf0
addedWeil's positivity criterion1b1a3e455e01
addedLi's criterionedfb8e622c1e
addedSpeiser's equivalence (zeros of zeta')360dba68f850
addedSimple critical-line zeros equivalencee96a2e244cc1
addedde Bruijn–Newman constantbaa5fd9bdf90
addedGrönwall: GRH implies Gauss's class-number-1 list complete7f4400ecd993
addedHardy–Littlewood (1917) on Chebyshev's bias under GRH6305ac95d9ed
addedHardy–Littlewood (1923) on ternary Goldbach under GRHc2c67033c4c4
addedChowla's bound on least prime in AP under GRH043bf6c585fa
addedHooley: GRH implies Artin's primitive-root conjecture76a82208c9c6
addedWeinberger: GRH implies idoneal-number list complete66d72bbadffe
addedWeinberger on class-number-1 number fields under GRH91283c6843a0
addedMiller test: polynomial-time primality under GRHb12e78b849c3
addedOno–Soundararajan on Ramanujan's form under GRHfe57aec7751b
addedDunn–Radziwiłł on Patterson's conjecture under GRHe3c3149e5edf
addedHecke (1918)b9b2d1a7ae4b
addedDeuring (1933)d1dbe8624d6d
addedMordell (1934)6d6f8e268031
addedHeilbronn (1934)7d2f17c0fcef
addedLittlewood's sign-change theorem for pi(x) - li(x)e4612e5cec60
addedNicolas inequality on Euler's totienta28ea310d424
addedRH for function fields (Artin, Hasse, Weil)9b75fa155ddb
addedGRH for arithmetic zeta functions of arithmetic schemesadeb0ff6a392
addedSelberg's RH analogue for Selberg zeta functionsf8f85740d939
addedRamanujan graph characterization via Ihara zeta1096b95781d9
addedMontgomery's pair correlation conjecture7a2e7f1fbb19
addedMontgomery: at least 2/3 of zeros are simple under RH74d285cabd80
addedRH for Goss zeta functions (Sheats)07dd1344098a
addedMain conjecture of Iwasawa theory3afcf210e71d
addedRiemann–von Mangoldt formula for N(T)7ab7ad54e379
addedTrudgian's explicit bound on N(T)04777f6b7291
addedKaratsuba's sign-change theorem for S(t)96311841d14d
addedSelberg's moment formula for S(T)2c52fda53f80
addedHadamard–de la Vallée-Poussin: no zeros on Re(s)=1dbae53a10684
addedDe la Vallée-Poussin classical zero-free region74054665f154
addedMossinghoff–Trudgian–Yang zero-free regions02d9270b1c06
addedHardy: infinitely many zeros on the critical linea1002fce9173
addedSelberg: positive proportion of zeros on critical line1112a6fbb4ff
addedLevinson: one-third of zeros on critical line39eb4032cafd
addedConrey: two-fifths of zeros on critical linee8cef287de30
addedPratt–Robles–Zaharescu–Zeindler: five-twelfths on critical line7fe88c8b60ca
addedBohr–Landau zero density estimate593a2224a8cf
addedHardy's infinitely-many-real-zeros theoremfdf32af997fe
addedHardy–Littlewood conjectures on real zerosd271ddf10ab9
addedSelberg's zeta function conjecture (Selberg's lower bound)52ded94919cf
addedKaratsuba's proof of Selberg's conjecturedbe5956f1d1d
addedKaratsuba's almost-all-intervals analog of Selberga3be48080b27
addedHardy's Z function and Riemann–Siegel theta11ab3839e911
addedGram point42e1c4803163
addedGram's lawf288add86a86
addedGood Gram pointa4b93d9eb629
addedGram blocke2ef5419fca4
addedRosser's ruleb5cc11c68207
addedTrudgian: positive proportion of failures of Gram/Rosserae81ee108d3c
addedKatz–Sarnak symmetry-type philosophy for L-functions594f54b03f4c
addedKeating–Snaith moments conjectureff1c1243a4e5