2021 SOLUTIONS
2021 LOOK BACK
2020 SOLUTIONS
RIEMANN HYPOTHESIS
NSE & 0-POINT ENERGY
YME & 0-POINT ENERGY
ENTROPY & 0-P. ENERGY
PLASMA HEATING
MHD
WHO I AM
LITERATURE
literature (RH & Goldbach)
literature (general)


books:

Edwards H. M., Riemann's Zeta Function, Dover Publications, Inc., Mineola, New York, 2001

Titchmarsh E. C., The Theory of the Riemann Zeta-function, Clarendon Press, Oxford, 1986


internet links:

http://www.digizeitschriften.de

http://www.imsc.res.in/~rao/ramanujan/CamUnivCpapers/collectedright1.htm


previous OVERVIEW pages

          

Braun K., RH, YME, NSE, GUT solutions, overview, Oct 31, 2019

          

Braun K., RH, YME, NSE, GUT, OVERVIEW page, June 30, 2019

          

Braun K., RH, YME, NSE, GUT, OVERVIEW page, Feb 2019


        

Braun K., RH, YME, NSE, GUT, OVERVIEW page, Jan 2019

        

Braun K., RH, YME, NSE, GUT, OVERVIEW page, Dec 2018
  

     

Braun K., Three Millennium problems, RH, NSE, YME, OVERVIEW

    

Braun K., A distributional way to prove the Goldbach conjecture leveraging the circle method
 

  

Axler C., On a Family of Functions Defined Over Sums of Primes

  

Balasubramanian R., Siegel Zeros and the Goldbach Problem


  

Binham N. H., Szegoe s theorem and H(1 2)


  

Chaudhury K. N., On the Hilbert Transforms of Wavelets
 

  

Chen Distance function wavelets part 1


  

Derezinski J., Richard S., On Radial Schroedinger Operators with a Coulomb Potential

  



Chakraborty K., Hoque A., Quadratic reciprocity and some non-differentiable functions



Dahlke S., Maass P., The Affine Uncertainty Principle in One and Two Dimensions


Dahlke S., Weinreich I., Wavelet Bases Adapted to Pseudodifferential Operators


Glowinski R. et al., wavelet methods in computational fluid dynamics



Holschneider M., Tchamitchian, Pointwise analysis of Riemann s nondifferentiable function



Jaffard S., The spectrum of singularities of Riemann s function



Bedrosian E., A product theorem for Hilbert transform


Bateman H., The mathematical analysis of electrical and optical wave-motion on the basis of Maxwells equations


M.V. Berry I.P. Keating H=xp and Riemann zeros


Berndt B. C., Ramanujan's Notebooks I


Berndt B. C., Ramanujan's Notebooks II


Berndt B. C., Ramanujan's Notebooks III


Bernd B. C., Ramanujan's Notebooks IV


Bernstein I. B., Greene J. M., Kruskal M. D., Exact Nonlinear Plasma Oscillations



Hauray M., Mean field limit for the one dimensional Vlasov-Poisson equation


Bertrand J., The Mellin Transform


P. Biane et.al. Probability laws related to Jacobi-Theta, Riemann Zeta functions ...


Bingham Inoue An Abel-Tauber theorem for hankel transform


Bohr Die Riemannsche Zetafunktion


E. Bombieri J. Lagarias Complements of Li`s criterion for the Riemann Hypothesis


Boros G., Moll V. H., sums of arctangents and some formulas of Ramanujan


D. Bump et al. A Local Riemann Hypothesis I

 

J.-F. Burnol On Fourier and Zeta(s)


ButzerJansche A Direct approach to the Mellin Transform.pdf


Cardon Convolution operators and zeros of entire functions



Chouly F., et. all, An overview of recent results on Nitsche s method for contact problems



Costabel M., Coercive Bilinear Form for Maxwell s Equations
 


Csardas G., Fourier transforms of positive definite kernels and the Riemann Zeta-Function


Deshouiliers J.-M., A complete Vinogradov 3-Primes theorem under the Riemann Hypothesis


D. Dickinson On Lommel and Bessel Polynomials.pdf


Dixit A., Moll V. H., The integrals in Gradshteyn and Ryzhik. Part 28 The confluent hypergeometric function and Whittaker functions


G. Doetsch Ueber die Singularitaeten der Mellin-Transformierten


G. Doetsch Summatorische Eigenschaft der Bessel Fkt ....


Duistermaat J. J., Selfsimilarity of Riemann s Nondifferentiable Function


Duffin Weinberger Dualization Poisson Summation Formula.pdf


Duffin R. J., Yukawan potential theory

     

Ebenfelt P., Khavinson D., Shapiro H. S., An inverse problem for the double layer potential


Endres S., Steiner F., A new proof of the Voronoi summation formula

  

Erdös P., On the distribution functions of additive functions


 

Erdös P., Kac M., The Gaussian Law of Errors in the Theory of Addtive Number Theoretic Functions


 

Erdös P., On additive arithmetical functions and applications of probability to number theory
 

      

Farge M., Schneider K., Wavelet transforms and their applications to MHD and plasma turbulence, a review


Federbush P., Navier and Stokes meet the Wavelet


Fichera G., Boundary Value Problems of Elasticity with Unilateral Constraints



Friedrich H., Cauchy Problem for the Conformal Vacuum Field Equations in General Relativity


Fourier theory of cardinal functions


Gaier D., Konstruktive Methoden der konformen Abbildung

 

Galambos J., Distribution of arithmetical functions. A survey


R. Garunkstis On the Voronin s universality theorem for the Riemann Zeta-function.pdf


Gaspers G., Using integrals of squares of certain real-valued special functions to prove that .....


Gautschi W., Waldvogel J., Computing the Hilbert Transform of the Generalized Laguerre and Hermite Weight Functions

Geshwind Pseudodifferential Operators on SU(2).pdf



Goedel K., An Example of a New Type of Cosmological Solutions of Einstein´s Field Equations of Gravitation


Goldston D. A., On Hardy and Littlewood Contribution to the Goldbach Conjecture


Gomes J., Vilbo L., From Fourier Analysis to Wavelets, Course Notes


Hamburger Ueber Beziehungen die mit Funktionalgleichung aequivalent sind


Hardy G. H., Littlewood J. E., SomeProblems of Partitio Numerorum III, On the Expression of a Number as a Sum of Primes

 

Hofmann S. et all, L(p) bounds for the Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds

   

Helfgott H. A., Major Arcs for Goldbach s Prpblem


   

Helfgott H. A., Minor Arcs for Goldbach s Prpblem
 


M. Johansson The Hilbert transform.pdf


On the Hilbert Transforms of Wavelets


Kac M., Probability methods in some problems of analysis and number theory

 

Kac M., Statistical Independence in Probability, Analysis and Number Theory

  

Kang H., Kawagoe, Surface Riesz transforms and spectral property of elastic Neumann-Poincare operators on less smooth domains in three dimensions


Karlsson A., Applications of the heat kernels on abelian groups, Zeta(2n), quadratic reciprocity, Bessel integrals

   

Kasch F., Abschätzungen der Dichte von Summenmengen, I


   

Kasch F., Abschätzungen der Dichte von Summenmengen, II


   

Kasch F., Abschätzungen der Dichte von Summenmengen, III
 

   

Kim, H., Origin of the Universe, A Hint from Eddington-inspired Born-Infeld gravity

    

Kneser H., Geschlossene Flaechen in dreidimensionalen Mannigfaltigkeiten


Koch Ueber die Riemannsche Primzahlfunktion


Korevaar J., Prime pairs and the zeta function


Korevaar, J., Distributional Wiener Ikehara theorem and the twin primes


Kowalenko V., Frankel N. E., Asymptotics for the Kummer Function of Bose Plasmas


P. Kurlberg A local Riemann Hypothesis, II


Landau E., Handbuch der Lehre von der Verteilung der Primzahlen I


Landau E., Handbuch der Lehre von der Verteilung der Primzahlen II


Landau E., Zur Goldbachschen Vermutung


Landau E., die Goldbachsche Vermutung und der Schnirelmannsche Satz

 

Landau E., Ueber die zahlentheoretische Function und ihre Beziehung zum Goldbachschen Satz

 

Landau E., Ueber eine trigonometrische Reihe
 

 

Landau E., Ueber die Fareyreihe und die Riemannsche Vermutung



 


Lebedev N. N., Special Functions and their Applications


Lucke B., Zur Hardy-Littlewoodschen Behandlung des Goldbachschen Problems I


Lucke B., Zur Hardy-Littlewoodschen Behandlung des Goldbachschen Problems II


Mashreghi J., Hilbert transform of logf



Maxwell J. C., A Dynamical Theory of the Electromagnetic Field


McMullen C., Complex Analysis


Mellin Abriss einer einheitlichen Theorie der Gamma und hypergeometrischen Fktn


Miller S. D., Schmid W., Summation Formulas, from Poisson and Voronoi to the Present


Nag S., Sullivan D., Teichmüller theory and the universal period mapping via quantum calculus and the H(1 2) space on the circle


Nasim C., On the summation Formula of Voronoi



Nitsche J. A., lecture notes I, Approximation Theory in Hilbert Scales

 

Nitsche J. A., lecture notes II, Extensions and Generalizations



http://www.archive.org/stream/handbuchgamma00nielrich/handbuchgamma00nielrich_djvu.txt



Oskolov K. I., Chakhiev M. A., On Riemann Nondifferentiable Function and Schroedinger Equation



    

Nitsche J. A., 1988, Direct Proofs of Some Unusual Shift-Theorems

     

Nitsche J. A., Free boundary problems for Stokes´s flows and finite element methods

     

Pathak R. S., Singh A., Distributional Wavelet Transform

 

Petersen Abelian and Tauberian Theorems Philosophy


B. Petersen Introduction to the FT and Pseudo-differential Operators distribution valued holomorphic functions I.pdf


B. Petersen Introduction to the FT and Pseudo-differential Operators distribution valued holomorphic functions II.pdf


Pilipovic S., Stankovic B., Tauberian Theorems for Integral Transforms of Distributions


Pichler A., On a rapidly converging series for the Riemann Zeta function


Pollack D. Initial data for the Cauchy Problem in General Relativity, Lecture 2

   

Polya Ueber eine neue Weise bestimmte Integrale in der Zahlentheorie zu gebrauchen


Polya G., On the zeros of an integral function represented by Fourier integral.pdf


Polya G., On the zeros of certain trigonometric integrals.pdf


Polya G., Bemerkungen ueber die Integraldarstellung der Riemannschen Zeta-Funktion.pdf


Polya G., Ueber die algebraisch-funktionentheoretischen Untersuchungen von J. L. W. V. Jensen


Polya Trigonometrische Integrale mit nur reellen NS


Ramanujan's Lost Notebook Part IV


Ramanujan, New expressions for Riemann s functions

  

Renyi A., Probabilistic methods in number theory


Rice A., Goldbach s Problems


Riemann B., Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe


Rindler W., Relativity. Special, General, and Cosmological

   

Rohrbach H., Einige neuere Untersuchungen ueber die Dichte in der additiven ZahlentheorieRohrbach H., Einige neuere Untersuchungen ueber die Dichte in der additiven Zahlentheorie


W. Schnee Die Funktionalgleichung der Zetafunktion und der Dirichletschen Reihen mit periodischen Koeffizienten

   

Schoenberg I., Ueber die asymptotische Verteilung reeller Zahlen mod I


  

Schnirelmann L., Ueber additive Eigenschaften von Zahlen
 


Schulz W., Ueber die Galoissche Gruppe der Hermiteschen Polynome


Sedletskii A. M., Asymptotics of the Zeros of Degenerate Hypergeometric Functions


Sedletskii A. M., On the Zeros of Laplace Transfroms

    

Seifert H., Topologie dreidimensionaler gefaserter Raeume


Siegel C. L., Transcendental Numbers, Princeton University Press, 1949


Siegel Bemerkungen zu einem Satz von Hamburger über die Funktionalgleichung der Riemannschen Zeta Funktion


The confluent hypergeometric function


Vajjha K., On a Definite Integral of the Fractional Part Function


Vindas J., Estrada R., A quick distributional way to the prime number Theorem


Vindas J., Introduction to Tauberian theory, A distributional Approach


Weiss J., The Hilbert Transform of Wavelets are Wavelets



Werner P., Self-Adjoint Extensions of the Lapalce Operator with Respect to Electric and Magnetic Boundary Conditions



Werner P., Spectral Properties of the Laplace Operator with respect to Electric and Magnetic Boundary Conditions

 

   

Weyl H., Ueber die Gleichverteilung von Zahlen mod 1




Weyl H., Reine Infinitesimalgeometrie


Wolke D., Das Goldbachsche Problem

Riemann´s original paper:

handwritten paper from 1859 and its english translation


Riemann handwritten paper from 1859
     

Riemann article english