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Diamond, Harold George

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Author ID: diamond.harold-george Recent zbMATH articles by "Diamond, Harold George"
Published as: Diamond, Harold G.; Diamond, H. G.; Diamond, H.; Diamond, Harold George; Diamond, Harold D.; Diamond, Harold
Homepage: http://www.math.uiuc.edu/~hdiamond/
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Publications by Year

Citations contained in zbMATH Open

52 Publications have been cited 347 times in 218 Documents Cited by Year
Asymptotic distribution of Beurling’s generalized prime numbers. Zbl 0216.31403
Bateman, P. T.; Diamond, H. G.
35
1969
Estimates for partial sums of continued fraction partial quotients. Zbl 0589.10056
Diamond, Harold G.; Vaaler, Jeffrey D.
32
1986
Analytic number theory. An introductory course. Zbl 1074.11001
Bateman, Paul T.; Diamond, Harold G.
29
2004
Elementary methods in the study of the distribution of prime numbers. Zbl 0505.10021
Diamond, Harold G.
26
1982
Asymptotic distribution of Beurling’s generalized integers. Zbl 0186.36403
Diamond, H. G.
25
1970
A set of generalized numbers showing Beurling’s theorem to be sharp. Zbl 0186.36501
Diamond, Harold G.
15
1970
Combinatorial sieves of dimension exceeding one. Zbl 0639.10031
Diamond, H.; Halberstam, H.; Richert, H.-E.
14
1988
A higher-dimensional sieve method. With procedures for computing sieve functions. Zbl 1207.11099
Diamond, Harold G.; Halberstam, H.; Galway, William F.
13
2008
Beurling primes with large oscillation. Zbl 1207.11105
Diamond, Harold G.; Montgomery, Hugh L.; Vorhauer, Ulrike M. A.
11
2006
The prime number theorem for Beurling’s generalized numbers. Zbl 0167.32001
Diamond, H. G.
11
1969
Beurling generalized numbers. Zbl 1378.11002
Diamond, Harold G.; Zhang, Wen-Bin
10
2016
Generalized Euler constants. Zbl 1143.11036
Diamond, Harold G.; Ford, Kevin
10
2008
When do Beurling generalized integers have a density? Zbl 0355.10038
Diamond, Harold G.
9
1977
Sets on which an entire function is determined by its range. Zbl 0473.30022
Diamond, Harold G.; Pomerance, Carl; Rubel, Lee
7
1981
A PNT equivalence for Beurling numbers. Zbl 1318.11124
Diamond, Harold G.; Zhang, Wen-Bin
7
2012
Some applications of sieves of dimension exceeding 1. Zbl 0941.11034
Diamond, H.; Halberstam, H.
6
1997
\(M(x) = o(x)\) estimates for Beurling numbers. Zbl 1443.11201
Debruyne, Gregory; Diamond, Harold G.; Vindas, Jasson
5
2018
A converse of Taylor’s theorem. Zbl 0212.14502
Albrecht, F.; Diamond, H. G.
5
1971
Chebyshev estimates for Beurling generalized prime numbers. Zbl 0268.10036
Diamond, Harold G.
5
1973
A boundary value problem for a pair of differential delay equations related to sieve theory. I. Zbl 0717.11036
Diamond, H.; Halberstam, H.; Richert, H.-E.
5
1990
Combinatorial sieves of dimension exceeding one. II. Zbl 0856.11046
Diamond, H. G.; Halberstam, H.; Richert, H.-E.
5
1996
A boundary value problem for a pair of differential delay equations related to sieve theory. II. Zbl 0790.11070
Diamond, Harold G.; Halberstam, H.; Richert, H.-E.
4
1993
Oscillation of Mertens’ product formula. Zbl 1214.11102
Diamond, Harold G.; Pintz, János
4
2009
A boundary value problem for a pair of differential delay equations related to sieve theory. III. Zbl 0809.11050
Diamond, Harold G.; Halberstam, H.; Richert, H.-E.
4
1994
Changes of sign of \(\pi(x)-li x\). Zbl 0304.10025
Diamond, Harold G.
3
1975
On the oscillation theorems of Pringsheim and Landau. Zbl 0964.11037
Bateman, Paul T.; Diamond, Harold G.
3
2000
On the sieve parameters \(\alpha_\kappa\) and \(\beta_\kappa\) for large \(\kappa\). Zbl 0909.11041
Diamond, Harold G.; Halberstam, H.
3
1997
Sieve auxiliary functions. II. Zbl 0798.11035
Diamond, Harold G.; Halberstam, H.; Richert, H.-E.
3
1993
An elementary proof of the prime number theorem with a remainder term. Zbl 0195.33304
Diamond, Harold G.; Steinig, John
3
1970
Estimation of the sieve auxiliary functions \(q_ \kappa\) in the range \(1<\kappa<2\). Zbl 0801.34067
Diamond, Harold G.; Halberstam, H.; Richert, H.-E.
3
1994
Gauss sums and Fourier analysis on multiplicative subgroups of Z/q. Zbl 0515.10032
Diamond, Harold G.; Gerth, Frank III; Vaaler, Jeffrey D.
3
1983
On sharp elementary prime number estimates. Zbl 0453.10007
Diamond, Harold G.; Erdős, Paul
3
1980
The combinatorial sieve. Zbl 0568.10025
Diamond, H.; Halberstam, H.
2
1985
Constructive elementary estimates for \(M(x)\). Zbl 0477.10007
Diamond, Harold G.; McCurley, Kevin S.
2
1981
Optimality of Chebyshev bounds for Beurling generalized numbers. Zbl 1315.11086
Diamond, Harold G.; Zhang, Wen-Bin
2
2013
Functions with non-negative convolutions. Zbl 0377.42007
Diamond, Harold G.; Essen, Matts
2
1978
Chebyshev bounds for Beurling numbers. Zbl 1309.11069
Diamond, Harold G.; Zhang, Wen-Bin
2
2013
Characterization of derivations on an algebra of measures. Zbl 0145.38801
Diamond, H. G.
2
1967
Number theory for the millennium I. Proceedings of the millennial conference on number theory, Urbana-Champaign, IL, USA, May 21–26, 2000. Zbl 1002.00005
1
2002
A hundred years of prime numbers. Zbl 0871.11005
Bateman, Paul T.; Diamond, Harold G.
1
1996
On a Tauberian theorem of Wiener and Pitt. Zbl 0205.40704
Diamond, H. G.
1
1972
An extremal problem involving functions and their inverses. Zbl 0235.49007
Albrecht, Felix; Diamond, Harold G.
1
1972
The distribution of values of Euler’s phi function. Zbl 0273.10036
Diamond, Harold G.
1
1973
Monotonicity of the zero of the sieve auxiliary function \(\bar \chi_ \kappa\) in the range \(3/2 <\kappa <2\). Zbl 0815.11045
Diamond, Harold G.; Halberstam, H.; Richert, H.-E.
1
1995
A difference differential equation of Euler-Cauchy type. Zbl 0903.34056
Bradley, David M.; Diamond, Harold G.
1
1997
Differential inequalities for Iwaniec’s \(q\) functions. Zbl 0928.11039
Diamond, Harold G.; Halberstam, H.
1
1999
Sieve auxiliary functions. Zbl 0704.11031
Diamond, Harold G.; Halberstam, H.; Richert, H.-E.
1
1990
Bounds for the logarithm of the Euler gamma function and its derivatives. Zbl 1331.33002
Diamond, Harold G.; Straub, Armin
1
2016
A number theoretic series of I. Kasara. Zbl 0505.10024
Diamond, Harold G.
1
1984
Two results on Beurling generalized numbers. Zbl 1249.11097
Diamond, Harold G.
1
2011
Interpolation of the Dirichlet divisor problem. Zbl 0155.09401
Diamond, Harold George
1
1967
Characterization of derivations on an algebra of measures. II. Zbl 0167.14802
Diamond, H. G.
1
1968
\(M(x) = o(x)\) estimates for Beurling numbers. Zbl 1443.11201
Debruyne, Gregory; Diamond, Harold G.; Vindas, Jasson
5
2018
Beurling generalized numbers. Zbl 1378.11002
Diamond, Harold G.; Zhang, Wen-Bin
10
2016
Bounds for the logarithm of the Euler gamma function and its derivatives. Zbl 1331.33002
Diamond, Harold G.; Straub, Armin
1
2016
Optimality of Chebyshev bounds for Beurling generalized numbers. Zbl 1315.11086
Diamond, Harold G.; Zhang, Wen-Bin
2
2013
Chebyshev bounds for Beurling numbers. Zbl 1309.11069
Diamond, Harold G.; Zhang, Wen-Bin
2
2013
A PNT equivalence for Beurling numbers. Zbl 1318.11124
Diamond, Harold G.; Zhang, Wen-Bin
7
2012
Two results on Beurling generalized numbers. Zbl 1249.11097
Diamond, Harold G.
1
2011
Oscillation of Mertens’ product formula. Zbl 1214.11102
Diamond, Harold G.; Pintz, János
4
2009
A higher-dimensional sieve method. With procedures for computing sieve functions. Zbl 1207.11099
Diamond, Harold G.; Halberstam, H.; Galway, William F.
13
2008
Generalized Euler constants. Zbl 1143.11036
Diamond, Harold G.; Ford, Kevin
10
2008
Beurling primes with large oscillation. Zbl 1207.11105
Diamond, Harold G.; Montgomery, Hugh L.; Vorhauer, Ulrike M. A.
11
2006
Analytic number theory. An introductory course. Zbl 1074.11001
Bateman, Paul T.; Diamond, Harold G.
29
2004
Number theory for the millennium I. Proceedings of the millennial conference on number theory, Urbana-Champaign, IL, USA, May 21–26, 2000. Zbl 1002.00005
1
2002
On the oscillation theorems of Pringsheim and Landau. Zbl 0964.11037
Bateman, Paul T.; Diamond, Harold G.
3
2000
Differential inequalities for Iwaniec’s \(q\) functions. Zbl 0928.11039
Diamond, Harold G.; Halberstam, H.
1
1999
Some applications of sieves of dimension exceeding 1. Zbl 0941.11034
Diamond, H.; Halberstam, H.
6
1997
On the sieve parameters \(\alpha_\kappa\) and \(\beta_\kappa\) for large \(\kappa\). Zbl 0909.11041
Diamond, Harold G.; Halberstam, H.
3
1997
A difference differential equation of Euler-Cauchy type. Zbl 0903.34056
Bradley, David M.; Diamond, Harold G.
1
1997
Combinatorial sieves of dimension exceeding one. II. Zbl 0856.11046
Diamond, H. G.; Halberstam, H.; Richert, H.-E.
5
1996
A hundred years of prime numbers. Zbl 0871.11005
Bateman, Paul T.; Diamond, Harold G.
1
1996
Monotonicity of the zero of the sieve auxiliary function \(\bar \chi_ \kappa\) in the range \(3/2 <\kappa <2\). Zbl 0815.11045
Diamond, Harold G.; Halberstam, H.; Richert, H.-E.
1
1995
A boundary value problem for a pair of differential delay equations related to sieve theory. III. Zbl 0809.11050
Diamond, Harold G.; Halberstam, H.; Richert, H.-E.
4
1994
Estimation of the sieve auxiliary functions \(q_ \kappa\) in the range \(1<\kappa<2\). Zbl 0801.34067
Diamond, Harold G.; Halberstam, H.; Richert, H.-E.
3
1994
A boundary value problem for a pair of differential delay equations related to sieve theory. II. Zbl 0790.11070
Diamond, Harold G.; Halberstam, H.; Richert, H.-E.
4
1993
Sieve auxiliary functions. II. Zbl 0798.11035
Diamond, Harold G.; Halberstam, H.; Richert, H.-E.
3
1993
A boundary value problem for a pair of differential delay equations related to sieve theory. I. Zbl 0717.11036
Diamond, H.; Halberstam, H.; Richert, H.-E.
5
1990
Sieve auxiliary functions. Zbl 0704.11031
Diamond, Harold G.; Halberstam, H.; Richert, H.-E.
1
1990
Combinatorial sieves of dimension exceeding one. Zbl 0639.10031
Diamond, H.; Halberstam, H.; Richert, H.-E.
14
1988
Estimates for partial sums of continued fraction partial quotients. Zbl 0589.10056
Diamond, Harold G.; Vaaler, Jeffrey D.
32
1986
The combinatorial sieve. Zbl 0568.10025
Diamond, H.; Halberstam, H.
2
1985
A number theoretic series of I. Kasara. Zbl 0505.10024
Diamond, Harold G.
1
1984
Gauss sums and Fourier analysis on multiplicative subgroups of Z/q. Zbl 0515.10032
Diamond, Harold G.; Gerth, Frank III; Vaaler, Jeffrey D.
3
1983
Elementary methods in the study of the distribution of prime numbers. Zbl 0505.10021
Diamond, Harold G.
26
1982
Sets on which an entire function is determined by its range. Zbl 0473.30022
Diamond, Harold G.; Pomerance, Carl; Rubel, Lee
7
1981
Constructive elementary estimates for \(M(x)\). Zbl 0477.10007
Diamond, Harold G.; McCurley, Kevin S.
2
1981
On sharp elementary prime number estimates. Zbl 0453.10007
Diamond, Harold G.; Erdős, Paul
3
1980
Functions with non-negative convolutions. Zbl 0377.42007
Diamond, Harold G.; Essen, Matts
2
1978
When do Beurling generalized integers have a density? Zbl 0355.10038
Diamond, Harold G.
9
1977
Changes of sign of \(\pi(x)-li x\). Zbl 0304.10025
Diamond, Harold G.
3
1975
Chebyshev estimates for Beurling generalized prime numbers. Zbl 0268.10036
Diamond, Harold G.
5
1973
The distribution of values of Euler’s phi function. Zbl 0273.10036
Diamond, Harold G.
1
1973
On a Tauberian theorem of Wiener and Pitt. Zbl 0205.40704
Diamond, H. G.
1
1972
An extremal problem involving functions and their inverses. Zbl 0235.49007
Albrecht, Felix; Diamond, Harold G.
1
1972
A converse of Taylor’s theorem. Zbl 0212.14502
Albrecht, F.; Diamond, H. G.
5
1971
Asymptotic distribution of Beurling’s generalized integers. Zbl 0186.36403
Diamond, H. G.
25
1970
A set of generalized numbers showing Beurling’s theorem to be sharp. Zbl 0186.36501
Diamond, Harold G.
15
1970
An elementary proof of the prime number theorem with a remainder term. Zbl 0195.33304
Diamond, Harold G.; Steinig, John
3
1970
Asymptotic distribution of Beurling’s generalized prime numbers. Zbl 0216.31403
Bateman, P. T.; Diamond, H. G.
35
1969
The prime number theorem for Beurling’s generalized numbers. Zbl 0167.32001
Diamond, H. G.
11
1969
Characterization of derivations on an algebra of measures. II. Zbl 0167.14802
Diamond, H. G.
1
1968
Characterization of derivations on an algebra of measures. Zbl 0145.38801
Diamond, H. G.
2
1967
Interpolation of the Dirichlet divisor problem. Zbl 0155.09401
Diamond, Harold George
1
1967
all top 5

Cited by 247 Authors

14 Diamond, Harold George
14 Zhang, Wenbin
9 Debruyne, Gregory
9 Vindas, Jasson
8 Hilberdink, Titus W.
6 Kesseböhmer, Marc
5 Kahane, Jean-Pierre
4 Hildebrand, Adolf J.
4 Schindler, Tanja I.
3 Alkan, Emre
3 Ford, Kevin B.
3 Gadre, Vaibhav S.
3 Halberstam, Heini
3 Kontorovich, Alex V.
3 Nakada, Hitoshi
3 Ramaré, Olivier
3 Sarnak, Peter Clive
2 Aaronson, Jon
2 Balazard, Michel
2 Bazzanella, Danilo
2 Berkes, István
2 Bradley, David M.
2 Broucke, Frederik
2 Chatterjee, Tapas
2 de Camargo, André Pierro
2 Dikranjan, Dikran N.
2 Franze, C. S.
2 Garunkštis, Ramūnas
2 Gun, Sanoli
2 Halbeisen, Lorenz J.
2 Haynes, Alan K.
2 Horváth, Lajos
2 Hungerbuhler, Norbert
2 Khurana, Suraj Singh
2 Korevaar, Jacob
2 Lagarias, Jeffrey C.
2 Lichtman, Jared Duker
2 Ma, Liangang
2 Müller, Helmut
2 Natsui, Rie
2 Neamah, Ammar Ali
2 Nevo, Amos
2 Pintz, Janos
2 Saha, Ekata
2 Schumacher, Salome
2 Slassi, Mehdi
2 Sofos, Efthymios
2 Stankus, Eugenijus
2 Takashima, Keizo
2 Tenenbaum, Gérald
2 Wang, Biao
2 Wang, Yuchao
2 Zhang, Zhenliang
1 Ablaev, Farid M.
1 Acikgoz, Mehmet
1 Adan, Ivo J. B. F.
1 Aharoni, Ron
1 Al-Maamori, Faez Ali
1 Albeverio, Sergio A.
1 Araci, Serkan
1 Athreya, Jayadev S.
1 Athreya, Krishna Balasundaram
1 Balanzario, Eugenio P.
1 Bănescu, Magdalena
1 Banks, William D.
1 Barile, Margherita
1 Barone, Fiorella
1 Bayless, Jonathan
1 Bazarova, Alina
1 Berarducci, Alessandro
1 Beresnevich, Victor V.
1 Bernstein, Daniel Julius
1 Bharadwaj, Abhishek T.
1 Bingham, Nicholas Hugh
1 Birkner, Peter
1 Bondarenko, Andriy V.
1 Booker, Andrew R.
1 Borel, Jean-Pierre
1 Borwein, Peter Benjamin
1 Bourgain, Jean
1 Boussaf, Kamal
1 Bremer, James C.
1 Bröker, Reinier
1 Browning, Timothy Daniel
1 Brüdern, Jörg
1 Brunotte, Horst
1 Byrnes, James S.
1 Cai, Zhaodong
1 Cebulla, Christof
1 Ching, Tak Wing
1 Chmielowska, Agata
1 Choi, Stephen Kwok-Kwong
1 Ciesielski, Krzysztof Chris
1 Clark, Peter Louis
1 Cook, Brian
1 Coons, Michael
1 Coutin, Laure
1 Davydov, Youri
1 de la Bretèche, Régis
1 de Roton, Anne
...and 147 more Authors
all top 5

Cited in 90 Serials

32 Journal of Number Theory
9 Transactions of the American Mathematical Society
9 International Journal of Number Theory
8 Proceedings of the American Mathematical Society
7 Mathematische Zeitschrift
6 Acta Arithmetica
6 Monatshefte für Mathematik
5 Lithuanian Mathematical Journal
5 Journal de Théorie des Nombres de Bordeaux
4 Linear Algebra and its Applications
4 Bulletin of the American Mathematical Society. New Series
4 The Ramanujan Journal
3 Periodica Mathematica Hungarica
3 Mathematika
3 Acta Mathematica Hungarica
3 Journal of the European Mathematical Society (JEMS)
3 Stochastics and Dynamics
2 Discrete Mathematics
2 International Journal of Mathematical Education in Science and Technology
2 Israel Journal of Mathematics
2 Journal d’Analyse Mathématique
2 Journal of Mathematical Analysis and Applications
2 Mathematical Proceedings of the Cambridge Philosophical Society
2 Nonlinearity
2 Rocky Mountain Journal of Mathematics
2 Mathematics of Computation
2 Compositio Mathematica
2 Functiones et Approximatio. Commentarii Mathematici
2 Inventiones Mathematicae
2 Journal of Differential Equations
2 Manuscripta Mathematica
2 Mathematische Annalen
2 Michigan Mathematical Journal
2 Rendiconti del Circolo Matemàtico di Palermo. Serie II
2 Topology and its Applications
2 Ergodic Theory and Dynamical Systems
2 Journal of Theoretical Probability
2 Stochastic Processes and their Applications
2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
2 Experimental Mathematics
2 Annales Mathématiques Blaise Pascal
2 Integers
2 Research in Number Theory
1 Bulletin of the Australian Mathematical Society
1 Journal of Computational Physics
1 Linear and Multilinear Algebra
1 Chaos, Solitons and Fractals
1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
1 Acta Mathematica
1 Advances in Mathematics
1 Annales de l’Institut Fourier
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 Archiv der Mathematik
1 Commentarii Mathematici Helvetici
1 Duke Mathematical Journal
1 Journal of Algebra
1 Journal of Approximation Theory
1 Journal of Functional Analysis
1 Journal für die Reine und Angewandte Mathematik
1 Mathematische Nachrichten
1 Mathematica Slovaca
1 Memoirs of the American Mathematical Society
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Pacific Journal of Mathematics
1 European Journal of Combinatorics
1 Acta Applicandae Mathematicae
1 Journal of Cryptology
1 Queueing Systems
1 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série
1 IMRN. International Mathematics Research Notices
1 Expositiones Mathematicae
1 Indagationes Mathematicae. New Series
1 Fractals
1 Bulletin des Sciences Mathématiques
1 Complexity
1 Bernoulli
1 The Journal of Fourier Analysis and Applications
1 Journal of Integer Sequences
1 Lobachevskii Journal of Mathematics
1 Dynamical Systems
1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
1 Communications on Pure and Applied Analysis
1 Bulletin of the Brazilian Mathematical Society. New Series
1 Advances in Difference Equations
1 Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
1 Open Mathematics
1 Discrete Analysis
1 Proceedings of the American Mathematical Society. Series B
1 Annales Henri Lebesgue

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