Riemann Hypothesis
Unified Field Theory
literature II
literature III
Who I am

Literature I


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)


Buterin S. A. et al., Lectures on the theory of entire functions


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


Bernays P., Über die Darstellung von positiven, ganzen Zahlen durch die primitiven, binären quadratischen Formen ....


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


Berndt B. C., the Rogers-Ramanujan identities


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


Blohmann C., et all, Groupoid symmetry and constraints in general relativity


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


Brand H., Idealtheorie in Quaternionenalgebren


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


Carlitz L., Note on irregular primes


L. Carlitz, Some theorems on Kummer s congruences

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


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


Chen Distance function wavelets part 1

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


(CoG) Cornell G., et al., Modular Forms and Fermat s Last Theorem, p. 508-516


Coan B., Perng C., Factorization of Hurwitz Quaternions


(CoJ) Coates J., Sujatha R., Cyclotomic fields and zeta values


Costabel M., Coercive Bilinear Form for Maxwell s Equations


Craven T. et al., Zeros of derivatives of entire functions


Crisan D., Erban R., On the counting function of semiprimes

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


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


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


Dedekind R, Ueber die Anzahl der Idealklassen in reinen kubischen Zahlkörpern


van Delden, J., An estimate on the density of semiprimes pq in an interval of fixed width


Derezinski J., On radial Schroedinger operators with a Coulomb potential

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


Dunn A., Radziwill M., Bias in cubic Gauss sums, Patterson s conjecture


Ebbinghaus H., et al., Zahlen


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


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


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


Hasse H., Die Kummersche Vermutung fuer kubische Charaktere nach einem Primzahlmodul

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


Heath-Brown D. R., Patterson S. J., The distribution of Kummer sums at prime arguments


Hecke E., Analytische Arithmetik der positiven quadratischen Formen


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

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


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


Hurwitz, Vorlesungen über die Zahlentheorie der Quaternionen, Rezension

Ishmukhametov Sh., T., Sharifullina F. F., On Distribution of Semiprimes Numbers


Jaffard S., A Density Criterion for Frames of Complex Exponentials


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


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


Kirchhoff G., Ueber die Bewegung eines Rotationskörpers in einer Fluessigkeit


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


Koecher M., Remmert R., Hamilton s Quaternions


Korevaar J., Prime pairs and the zeta function

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


Koskivaara O., The Hilbert Transform

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


Krishnaswami G., Sachdev S., Algebra and geometry of Hamiltons quaternions


Kuipers J. B., Quaternions and rotation sequences


Kummer E. E., Zur Theorie der complexen Zahlen

Kummer E. E., Ueber die Zerlegung der aus Wurzeln der Einheit gebildeten complexen Zahlen in ihre Primfactoren


Kummer E. E., 6. Bestimmung der Anzahl nicht aequivalenter Classen fuer die aus Wurzeln der Einheit ....

Kummer E. E., 7. Zwei besondere Untersuchungen ueber die Classen-Anzahl und ueber die Einheiten der aus .. gebildeten complexen Zahlen


Kummer E. E., 8. Allgemeiner Beweis des Fermatschen Satzes .....


Kummer s main theorem


Kummer s work on cyclotomic fields


Kummer s irregularity index

Kummer E., Beitrag zur Theorie der Gamma Function


Kummer E. E., De residuis cubicis disquisitiones nonnnullae analyticae


Kummer E. E., Eine Aufgabe, betreffend die Theorie der cubischen Reste


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


Luca F. et. al., On the counting function of irregular primes

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


Mezo I., A note on the zeros and local extrema of Digamma related functions

Mellin Abriss einer einheitlichen Theorie der Gamma und hypergeometrischen Fktn


Milne J. S., Class Field Theory, lecture notes, August 6, 2020

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


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


Peters M., Darstellungen durch definite tertiäre quadratische Formen


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


Pichler A., Analytic Number Theory, Lecture Notes, Selected Topics

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


Ribenboim P., Die Welt der Primzahlen, S. 229-233


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


Stammbach U., Die eindeutige Primfaktorenzerlegung


The confluent hypergeometric function


Tong H., Introducing Quaternions to Integer Factorization


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


Waerden van, B., Die Reduktionstheorie der positiven quadratischen Formen


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