Revision #650 → #1542 · back to history
addedRiemann zeta function (lead definition)adcdff456be4
addedIrrationality of ζ(3) (Apéry)4420b5fb94ef
addedDefinition of ζ(s)4db08b2f74fd
addedDefinition via analytic continuationbe648ccc989d
addedAnalytic continuation to s ≠ 1c9f90e2f9fa9
addedMeromorphic with simple pole at s=16932af6f8396
addedEuler product formulad7f4ef10b963
addedInfinitely many primes4987b774fa06
addedSum of reciprocals of primes diverges7a19c77a6854
addedDensity of primes is zero2f0b9feabb0a
addedProbability of coprimalityc775aff4ec66
addedRiemann functional equation22924a04f769
addedTrivial zeros at negative even integers65266a372e2a
addedSymmetric functional equation (xi function)9c6909c3311c
addedTrivial zeros1cfbf17ff916
addedCritical stripd17de46ae285
addedCritical lineafd84975823c
addedRiemann hypothesis22a7a3d8a2bb
addedConrey: >40% on critical linef0214b2aac58
addedTrudgian count of zeros N(T)4bd18927a7dd
addedHardy: infinitely many real zeros783224b13694
addedHardy–Littlewood first conjecture38b56cac67c5
addedHardy–Littlewood second conjecturede4adcf0b346
addedPNT equivalent to no zeros on Re(s)=18baa09940ec2
addedKorobov–Vinogradov zero-free regiondcbdd3839b20
addedPlatt–Trudgian computational zero-free region2486a46aa8b0
addedMossinghoff–Trudgian–Yang zero-free region5daff0027846
addedYang zero-free region849f2adeb1be
addedBellotti zero-free region (after Ford)f7ca642ab035
addedBellotti large |t| zero-free region46c755ffba2c
addedInfinitely many zeros on critical line4a6f0f94fb89
addedLittlewood on imaginary parts of zeros9d0c5c4af184
addedCritical line theoremc90d40daf68b
addedFirst nontrivial zero26a9441671f5
addedZeros symmetric about real axisc8b8100db8b8
addedNontrivial zeros symmetric about critical linebf4db83fd92e
addedNo zeros on line Re(s)=1a278c6d8bd49
addedGrosswald–Schnitzer modified zeta functions55370576da16
addedValues at even positive integerse67a488a87a3
addedBasel problem ζ(2)17eadfe64cca
addedProbability two numbers are coprime199720b8e195
addedApéry's constant ζ(3)bf09c38d9257
addedValues at nonpositive integers9240d10d6cd3
addedVanishing at negative even integers9d604587e851
addedζ(−1) and 1+2+3+⋯a2dd76c0edf8
addedζ(0) and 1+1+1+⋯d8b84ed2ed3e
addedValue used in kinetic boundary layer problems2609221defc8
addedCauchy principal value equals Euler–Mascheroni488d1834bcc6
addedLimit at +∞ and essential singularity2711e1196f0b
addedReciprocal via Möbius function60d2e62f6f8d
addedRH equivalent to Möbius series validitycce448e466fc
addedZeta universality (Voronin)4b180f520e84
addedFunctions F and Gd6f1d83b2783
addedKaratsuba estimates of F and G198a086029fb
addedArgument S(t) of zeta8dd5db0942d0
addedSign changes of S(t)401324538a45
addedRearranged Dirichlet series (Re s > 0)210442ad6e94
addedRising-factorial series on whole plane933197e7f894
addedMellin transform4c9cf719cc1d
addedZeta as Mellin-type integral (Re s > 1)768a8a34ee26
addedRiemann contour integral for all s01d8e651362a
addedIntegral with prime-counting functionf404e576702c
addedMellin transform with Riemann J(x)760091358181
addedZeta via Jacobi theta function7213af480d5c
addedRegularized theta expressione470952337da
addedLaurent series about s=12990db5e7cb3
addedStieltjes constantsf68927079894
addedAbel–Plana integral relation259aaad2fbe8
addedHadamard product expansionab6b162b45fb
addedSimpler Hadamard producta437fe9089d0
addedKnopp–Hasse globally convergent series279cec82b929
addedHasse second globally convergent series662e8e6df1da
addedMaślanka globally convergent seriesca0f23e4c332
addedAsymptotics of coefficients (saddle point)79f047c3ba1a
addedBáez-Duarte criterion for RH8df4e3909826
addedBorwein rapidly convergent seriesc1e097d6b0fc
addedSeries via the primorial7dbd40ad797a
addedSeries via incomplete poly-Bernoulli numbers4553addf0bcc
addedMellin transform of the Engel mapf28df4d09ec1
addedStochastic representation via Brownian motionf85c3a737b12
addedEuler–Maclaurin numerical algorithm248e01295cc8
addedApplications in applied statisticsa0ee7299e8ad
addedCasimir effect / zeta regularizationfdaa22d7c63f
addedMusical tuning / equal divisions of the octave8649e0d1d4b5
addedZeta at equidistant integers in series for constants42b5de3b8281
addedSeries for the lemniscate constantc69567479341
addedHurwitz zeta function4d3c02a76c94
addedPolylogarithm4a563e492100
addedLerch transcendentcd26a971047c
addedMultiple zeta functionsb01ee30dfda2