2015, Anneli Lax new mathematical library, ISBN 9780883856505, Volume 46., xi, 144 pages

Book

2016, ISBN 9781107101920, xi, 142

... in 1859, the so-called Riemann hypothesis, which remains one of the most important unsolved problems in mathematics...

Numbers, Prime | Riemann hypothesis

Numbers, Prime | Riemann hypothesis

Book

2017, Encyclopedia of mathematics and its applications, ISBN 9781108290784, Volume 164-165, 2 volumes

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics...

Riemann hypothesis

Riemann hypothesis

Book

2014, London Mathematical Society student texts, ISBN 1107047218, Volume 80, xii, 152 pages

This book provides a lucid exposition of the connections between non-commutative geometry and the famous Riemann Hypothesis, focusing on the theory of one-dimensional varieties over a finite field...

Geometry | Riemann hypothesis | Algebraic fields | Noncommutative differential geometry

Geometry | Riemann hypothesis | Algebraic fields | Noncommutative differential geometry

Book

11/2017, ISBN 1108178227

Book

Proceedings of the National Academy of Sciences - PNAS, ISSN 0027-8424, 3/2016, Volume 113, Issue 10, pp. 2603 - 2608

... of
(
). It has a functional equation relating
(
) to
. We prove the Riemann hypothesis for these polynomials...

Period polynomials | Modular forms | Riemann hypothesis | VALUES | modular forms | period polynomials | MULTIDISCIPLINARY SCIENCES | ZEROS | Polynomials | Research | Mathematical research | Riemann integral | Mathematics - Number Theory | Physical Sciences

Period polynomials | Modular forms | Riemann hypothesis | VALUES | modular forms | period polynomials | MULTIDISCIPLINARY SCIENCES | ZEROS | Polynomials | Research | Mathematical research | Riemann integral | Mathematics - Number Theory | Physical Sciences

Journal Article

2005, 1st ed., ISBN 9780375421365, x, 292

Book

11/2017, Volume 73, Issue 6, 1

Book Review

Applicable Algebra in Engineering, Communication and Computing, ISSN 0938-1279, 8/2019, Volume 30, Issue 4, pp. 275 - 284

.... One of the most important problems from the applicable point of view is whether extremal weight enumerators satisfy the Riemann hypothesis...

Artificial Intelligence | 12D10 | Theory of Computation | Invariant polynomial ring | Binomial moment | Extremal weight enumerator | Computer Hardware | Computer Science | Secondary 13A50 | Riemann hypothesis | Primary 11T71 | Symbolic and Algebraic Manipulation | Zeta function for codes | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | WEIGHT ENUMERATORS | COMPUTER SCIENCE, THEORY & METHODS

Artificial Intelligence | 12D10 | Theory of Computation | Invariant polynomial ring | Binomial moment | Extremal weight enumerator | Computer Hardware | Computer Science | Secondary 13A50 | Riemann hypothesis | Primary 11T71 | Symbolic and Algebraic Manipulation | Zeta function for codes | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | WEIGHT ENUMERATORS | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 01/2014, Volume 409, Issue 1, pp. 244 - 253

Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero...

Riemann Hypothesis | Resonance method | Omega theorems | Riemann zeta-function | MATHEMATICS | MATHEMATICS, APPLIED | ZETA-FUNCTION | EXTREME VALUES

Riemann Hypothesis | Resonance method | Omega theorems | Riemann zeta-function | MATHEMATICS | MATHEMATICS, APPLIED | ZETA-FUNCTION | EXTREME VALUES

Journal Article

2002, 1st American ed., ISBN 0374250073, 340

Book

Mathematics (Basel), ISSN 2227-7390, 2018, Volume 6, Issue 12, p. 289

...) well-known that the Riemann hypothesis is not sufficient to prove Andrica’s conjecture: ∀n≥1, is p n + 1 - p n ≤ 1 ? However, can one at least get tolerably close...

Andrica's conjecture | Prime gaps | Riemann hypothesis | Primes | MATHEMATICS | primes | prime gaps | Andrica’s conjecture

Andrica's conjecture | Prime gaps | Riemann hypothesis | Primes | MATHEMATICS | primes | prime gaps | Andrica’s conjecture

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 04/2011, Volume 44, Issue 14, pp. 145203 - 9

...), where beta is an inverse temperature. We formulate Riemann hypothesis (RH) as a property of the low-temperature Kubo-Martin-Schwinger (KMS...

PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Functions (mathematics) | Equivalence | Mathematical analysis | Quantum mechanics | Inequalities | Texts | Inverse | Dynamical systems | Quantum Algebra | Quantum Physics | Mathematics | Number Theory | Physics

PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Functions (mathematics) | Equivalence | Mathematical analysis | Quantum mechanics | Inequalities | Texts | Inverse | Dynamical systems | Quantum Algebra | Quantum Physics | Mathematics | Number Theory | Physics

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 08/2018, Volume 68, Issue 4, pp. 741 - 748

We prove that, under the Riemann hypothesis, a wide class of analytic functions can be approximated by shifts
+ i
),
∈ ℕ...

universality | Riemann hypothesis | Riemann zeta-function | weak convergence | Primary 11M06 | MATHEMATICS | ZEROS | Analytic functions | Hypotheses

universality | Riemann hypothesis | Riemann zeta-function | weak convergence | Primary 11M06 | MATHEMATICS | ZEROS | Analytic functions | Hypotheses

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 07/2020, Volume 148, Issue 7, pp. 2863 - 2875

We recast the classical Lindelof hypothesis as an estimate for the sums Sigma(n <= x) n(-it). This leads us to propose that a more general form of the Lindelof hypothesis may be true, one involving estimates for sums of the type Sigma...

MATHEMATICS | Lindelof hypothesis | MATHEMATICS, APPLIED | Riemann hypothesis

MATHEMATICS | Lindelof hypothesis | MATHEMATICS, APPLIED | Riemann hypothesis

Journal Article

Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences, ISSN 1364-503X, 08/2015, Volume 373, Issue 2047, p. 20140240

...). In this paper, we establish a new asymmetric criterion for the Riemann hypothesis (RH), expressed in terms of the invertibility...

Fractal strings | Riemann zeta function | Riemann hypothesis | Complex dimensions | Phase transitions | Symmetric and asymmetric criteria for the riemann hypothesis | complex dimensions | WEYL-BERRY CONJECTURE | RENORMALIZATION-GROUP | ZETA-FUNCTIONS | MINKOWSKI MEASURABILITY | MULTIDISCIPLINARY SCIENCES | phase transitions | fractal strings | DIRAC OPERATORS | ONE HEAR | TUBE FORMULAS | symmetric and asymmetric criteria for the Riemann hypothesis | COUNTING FUNCTION

Fractal strings | Riemann zeta function | Riemann hypothesis | Complex dimensions | Phase transitions | Symmetric and asymmetric criteria for the riemann hypothesis | complex dimensions | WEYL-BERRY CONJECTURE | RENORMALIZATION-GROUP | ZETA-FUNCTIONS | MINKOWSKI MEASURABILITY | MULTIDISCIPLINARY SCIENCES | phase transitions | fractal strings | DIRAC OPERATORS | ONE HEAR | TUBE FORMULAS | symmetric and asymmetric criteria for the Riemann hypothesis | COUNTING FUNCTION

Journal Article

The Rocky Mountain journal of mathematics, ISSN 0035-7596, 2016, Volume 46, Issue 2, pp. 435 - 442

In this short note, we give a proof of the Riemann hypothesis for the Goss v-adic zeta function zeta(v...

Riemann hypothesis | Goss zeta function | MATHEMATICS

Riemann hypothesis | Goss zeta function | MATHEMATICS

Journal Article

International Journal of Modern Physics A, ISSN 0217-751X, 12/2016, Volume 31, Issue 36, p. 1650201

We discuss a precise relation between the Veneziano amplitude of string theory, rewritten in terms of ratios of the Riemann zeta function, and two elementary criteria for the Riemann hypothesis...

Riemann zeta function | string amplitude | Hilbert-Pólya programme | Hilbert-Polya programme | NUMBERS | PHYSICS, NUCLEAR | AMPLITUDES | PHYSICS, PARTICLES & FIELDS | Physics

Riemann zeta function | string amplitude | Hilbert-Pólya programme | Hilbert-Polya programme | NUMBERS | PHYSICS, NUCLEAR | AMPLITUDES | PHYSICS, PARTICLES & FIELDS | Physics

Journal Article

Journal of number theory, ISSN 0022-314X, 12/2016, Volume 169, pp. 342 - 352

.... The main result is a suggestive equivalence between an asymptotic functional equation for these L-functions and the corresponding case of the Generalized Riemann Hypothesis...

Dirichlet L-functions | Functional equations | Generalized Riemann Hypothesis | L-functions of graphs | Cyclic graphs | MATHEMATICS

Dirichlet L-functions | Functional equations | Generalized Riemann Hypothesis | L-functions of graphs | Cyclic graphs | MATHEMATICS

Journal Article

Communications in number theory and physics, ISSN 1931-4523, 2018, Volume 12, Issue 3, pp. 409 - 490

.... We conjecture that all a-coefficients of the DAHA superpolynomials upon the substitution q bar right arrow qt satisfy the Riemann Hypothesis for sufficiently small q for uncolored algebraic knots, presumably for q <= 1/2 as a = 0...

Iterated torus links | Plane curve singularities | Hasse-Weil zeta-function | Hilbert scheme | Khovanov-Rozansky homology | Double affine Hecke algebras | Jones polynomials | Compactified Jacobians | Macdonald polynomial | Riemann hypothesis | HOMFLY-PT polynomials | compactified Jacobians | MATHEMATICS, APPLIED | ZETA-FUNCTIONS | MATRIX FACTORIZATIONS | plane curve singularities | PHYSICS, MATHEMATICAL | KNOTS | MATHEMATICS | TORUS | LINK HOMOLOGY | double affine Hecke algebras | iterated torus links

Iterated torus links | Plane curve singularities | Hasse-Weil zeta-function | Hilbert scheme | Khovanov-Rozansky homology | Double affine Hecke algebras | Jones polynomials | Compactified Jacobians | Macdonald polynomial | Riemann hypothesis | HOMFLY-PT polynomials | compactified Jacobians | MATHEMATICS, APPLIED | ZETA-FUNCTIONS | MATRIX FACTORIZATIONS | plane curve singularities | PHYSICS, MATHEMATICAL | KNOTS | MATHEMATICS | TORUS | LINK HOMOLOGY | double affine Hecke algebras | iterated torus links

Journal Article

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