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Bateman, Paul Trevier

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Author ID: bateman.paul-t Recent zbMATH articles by "Bateman, Paul Trevier"
Published as: Bateman, P. T.; Bateman, Paul; Bateman, Paul T.
External Links: MGP · Wikidata · Celebratio Mathematica · GND
Documents Indexed: 50 Publications since 1949, including 1 Book
Biographic References: 3 Publications

Publications by Year

Citations contained in zbMATH

40 Publications have been cited 449 times in 420 Documents Cited by Year
A heuristic asymptotic formula concerning the distribution of prime numbers. Zbl 0105.03302
Bateman, P. T.; Horn, Roger A.
78
1962
The equivalence of two conjectures in the theory of numbers. Zbl 0055.27503
Bateman, P. T.; Chowla, Sarvadaman
39
1954
Asymptotic distribution of Beurling’s generalized prime numbers. Zbl 0216.31403
Bateman, P. T.; Diamond, H. G.
36
1969
Analytic number theory. An introductory course. Zbl 1074.11001
Bateman, Paul T.; Diamond, Harold G.
26
2004
On Epstein’s zeta function. Zbl 0128.27004
Bateman, P. T.; Grosswald, E.
25
1964
Geometrical extrema suggested by a lemma of Besicovitch. Zbl 0043.16202
Bateman, Paul T.; Erdős, Paul
21
1951
The distribution of values of the Euler function. Zbl 0217.31901
Bateman, P. T.
20
1972
On the representations of a number as the sum of three squares. Zbl 0043.04603
Bateman, Paul T.
20
1951
Primes represented by irreducible polynomials in one variable. Zbl 0136.32902
Bateman, Paul T.; Horn, Roger A.
17
1965
Monotonicity of partition functions. Zbl 0074.03502
Bateman, Paul T.; Erdős, Pál
17
1956
On a theorem of Erdős and Szekeres. Zbl 0079.07104
Bateman, Paul T.; Grosswald, Emil
16
1958
A limit involving least common multiples. Zbl 1124.11300
Bateman, Paul; Kalb, Jeffrey; Stenger, Allen
14
2002
Waring’s problem for algebraic number fields and primes of the form \((p^ r -1)/(p^ d-1)\). Zbl 0107.03903
Bateman, Paul T.; Stemmler, Rosemarie M.
13
1962
Remark on a recent note on linear forms. Zbl 0083.03801
Bateman, P. T.
11
1958
Note on the coefficients of the cyclotomic polynomial. Zbl 0035.31102
Bateman, P. T.
11
1949
Remarks on the size of \(L(1,\chi)\). Zbl 0036.30702
Bateman, Paul T.; Chowla, S.; Erdős, Pál
10
1950
The analogue of the Pisot-Vijayaraghavan numbers in fields of formal power series. Zbl 0105.02801
Bateman, P. T.; Duquette, Alfred L.
9
1962
A remark on infinite groups. Zbl 0039.25103
Bateman, P. T.
7
1950
Decidability and undecidability of theories with a predicate for the primes. Zbl 0785.03002
Bateman, P. T.; Jockusch, C. G.; Woods, A. R.
6
1993
Some new old-fashioned modular identities. Zbl 0909.11018
Bateman, Paul T.; Knopp, Marvin I.
5
1998
Positive integers expressible as a sum of three squares in essentially only one way. Zbl 0558.10038
Bateman, Paul T.; Grosswald, Emil
5
1984
Some special trigonometrical series related to the distribution of prime numbers. Zbl 0116.26904
Bateman, P. T.; Chowla, Sarvadaman
5
1963
Averages of character sums. Zbl 0041.01904
Bateman, P. T.; Chowla, Sarvadaman
5
1950
The Erdős-Fuchs theorem on the square of a power series. Zbl 0353.10041
Bateman, Paul T.
4
1977
On the oscillation theorems of Pringsheim and Landau. Zbl 0964.11037
Bateman, Paul T.; Diamond, Harold G.
3
2000
On the size of the coefficients of the cyclotomic polynomial. Zbl 0547.10010
Bateman, P. T.; Pomerance, C.; Vaughan, R. C.
3
1984
Some numerical results on Fekete polynomials. Zbl 0301.10036
Bateman, Paul T.; Purdy, George B.; Wagstaff, Samuel S. jun.
3
1975
Eugene E. Kohlbecker and Jack P. Tull: On a theorem of Erdős and Fuchs in additive number theory. Zbl 0112.27405
Bateman, P. T.
3
1963
Proof of a conjecture of Grosswald. Zbl 0080.03602
Bateman, Paul T.
3
1958
Linear relations connecting the imaginary parts of the zeros of the zeta function. Zbl 0216.03601
Bateman, P. T.; Brown, J. W.; Hall, R. S.; Kloss, K. E.; Stemmler, R. M.
2
1971
Imaginary quadratic fields with unique factorization. Zbl 0100.03103
Bateman, Paul T.; Grosswald, Emil
2
1962
Partitions into primes. Zbl 0073.03101
Bateman, Paul T.; Erdős, Pál
2
1956
Sums of squares and the preservation of modularity under congruence restrictions. Zbl 1040.11018
Bateman, Paul T.; Datskovsky, Boris A.; Knopp, Marvin I.
1
2001
A hundred years of prime numbers. Zbl 0871.11005
Bateman, Paul T.; Diamond, Harold G.
1
1996
The asymptotic formula for the number of representations of an integer as a sum of five squares. Zbl 0857.11019
Bateman, Paul T.
1
1996
Sums of distinct squares. Zbl 0815.11048
Bateman, Paul T.; Hildebrand, Adolf J.; Purdy, George B.
1
1994
The new Mersenne conjecture. Zbl 0694.10005
Bateman, P. T.; Selfridge, J. L.; Wagstaff, S. S. jun.
1
1989
Prime numbers in arithmetic progressions with difference 24. Zbl 0127.26805
Bateman, P. T.; Low, Marc E.
1
1965
Sequences of mass distributions on the unit circle which tend to a uniform distribution. Zbl 0128.27303
Bateman, P. T.
1
1964
Theorems implying the non-vanishing of \(\sum \chi(m)m^{-1}\) for real residue-characters. Zbl 0228.10021
Bateman, Paul T.
1
1961
Analytic number theory. An introductory course. Zbl 1074.11001
Bateman, Paul T.; Diamond, Harold G.
26
2004
A limit involving least common multiples. Zbl 1124.11300
Bateman, Paul; Kalb, Jeffrey; Stenger, Allen
14
2002
Sums of squares and the preservation of modularity under congruence restrictions. Zbl 1040.11018
Bateman, Paul T.; Datskovsky, Boris A.; Knopp, Marvin I.
1
2001
On the oscillation theorems of Pringsheim and Landau. Zbl 0964.11037
Bateman, Paul T.; Diamond, Harold G.
3
2000
Some new old-fashioned modular identities. Zbl 0909.11018
Bateman, Paul T.; Knopp, Marvin I.
5
1998
A hundred years of prime numbers. Zbl 0871.11005
Bateman, Paul T.; Diamond, Harold G.
1
1996
The asymptotic formula for the number of representations of an integer as a sum of five squares. Zbl 0857.11019
Bateman, Paul T.
1
1996
Sums of distinct squares. Zbl 0815.11048
Bateman, Paul T.; Hildebrand, Adolf J.; Purdy, George B.
1
1994
Decidability and undecidability of theories with a predicate for the primes. Zbl 0785.03002
Bateman, P. T.; Jockusch, C. G.; Woods, A. R.
6
1993
The new Mersenne conjecture. Zbl 0694.10005
Bateman, P. T.; Selfridge, J. L.; Wagstaff, S. S. jun.
1
1989
Positive integers expressible as a sum of three squares in essentially only one way. Zbl 0558.10038
Bateman, Paul T.; Grosswald, Emil
5
1984
On the size of the coefficients of the cyclotomic polynomial. Zbl 0547.10010
Bateman, P. T.; Pomerance, C.; Vaughan, R. C.
3
1984
The Erdős-Fuchs theorem on the square of a power series. Zbl 0353.10041
Bateman, Paul T.
4
1977
Some numerical results on Fekete polynomials. Zbl 0301.10036
Bateman, Paul T.; Purdy, George B.; Wagstaff, Samuel S. jun.
3
1975
The distribution of values of the Euler function. Zbl 0217.31901
Bateman, P. T.
20
1972
Linear relations connecting the imaginary parts of the zeros of the zeta function. Zbl 0216.03601
Bateman, P. T.; Brown, J. W.; Hall, R. S.; Kloss, K. E.; Stemmler, R. M.
2
1971
Asymptotic distribution of Beurling’s generalized prime numbers. Zbl 0216.31403
Bateman, P. T.; Diamond, H. G.
36
1969
Primes represented by irreducible polynomials in one variable. Zbl 0136.32902
Bateman, Paul T.; Horn, Roger A.
17
1965
Prime numbers in arithmetic progressions with difference 24. Zbl 0127.26805
Bateman, P. T.; Low, Marc E.
1
1965
On Epstein’s zeta function. Zbl 0128.27004
Bateman, P. T.; Grosswald, E.
25
1964
Sequences of mass distributions on the unit circle which tend to a uniform distribution. Zbl 0128.27303
Bateman, P. T.
1
1964
Some special trigonometrical series related to the distribution of prime numbers. Zbl 0116.26904
Bateman, P. T.; Chowla, Sarvadaman
5
1963
Eugene E. Kohlbecker and Jack P. Tull: On a theorem of Erdős and Fuchs in additive number theory. Zbl 0112.27405
Bateman, P. T.
3
1963
A heuristic asymptotic formula concerning the distribution of prime numbers. Zbl 0105.03302
Bateman, P. T.; Horn, Roger A.
78
1962
Waring’s problem for algebraic number fields and primes of the form \((p^ r -1)/(p^ d-1)\). Zbl 0107.03903
Bateman, Paul T.; Stemmler, Rosemarie M.
13
1962
The analogue of the Pisot-Vijayaraghavan numbers in fields of formal power series. Zbl 0105.02801
Bateman, P. T.; Duquette, Alfred L.
9
1962
Imaginary quadratic fields with unique factorization. Zbl 0100.03103
Bateman, Paul T.; Grosswald, Emil
2
1962
Theorems implying the non-vanishing of \(\sum \chi(m)m^{-1}\) for real residue-characters. Zbl 0228.10021
Bateman, Paul T.
1
1961
On a theorem of Erdős and Szekeres. Zbl 0079.07104
Bateman, Paul T.; Grosswald, Emil
16
1958
Remark on a recent note on linear forms. Zbl 0083.03801
Bateman, P. T.
11
1958
Proof of a conjecture of Grosswald. Zbl 0080.03602
Bateman, Paul T.
3
1958
Monotonicity of partition functions. Zbl 0074.03502
Bateman, Paul T.; Erdős, Pál
17
1956
Partitions into primes. Zbl 0073.03101
Bateman, Paul T.; Erdős, Pál
2
1956
The equivalence of two conjectures in the theory of numbers. Zbl 0055.27503
Bateman, P. T.; Chowla, Sarvadaman
39
1954
Geometrical extrema suggested by a lemma of Besicovitch. Zbl 0043.16202
Bateman, Paul T.; Erdős, Paul
21
1951
On the representations of a number as the sum of three squares. Zbl 0043.04603
Bateman, Paul T.
20
1951
Remarks on the size of \(L(1,\chi)\). Zbl 0036.30702
Bateman, Paul T.; Chowla, S.; Erdős, Pál
10
1950
A remark on infinite groups. Zbl 0039.25103
Bateman, P. T.
7
1950
Averages of character sums. Zbl 0041.01904
Bateman, P. T.; Chowla, Sarvadaman
5
1950
Note on the coefficients of the cyclotomic polynomial. Zbl 0035.31102
Bateman, P. T.
11
1949
all top 5

Cited by 541 Authors

10 Zhang, Wenbin
9 Luca, Florian
8 Hong, Shaofang
7 Diamond, Harold George
7 Garcia, Stephan Ramon
7 Hilberdink, Titus W.
7 Vindas, Jasson
6 Debruyne, Gregory
6 Qian, Guoyou
6 Shparlinski, Igor E.
5 Cooper, Shaun
5 Shanks, Daniel C.
4 Bateman, Paul Trevier
4 Evans, Anthony B.
4 Hbaib, Mohamed
4 Korevaar, Jacob
4 Vaughan, Robert C.
3 Bros, Jacques
3 Grosswald, Emil
3 Ichimura, Humio
3 Körner, Otto
3 Ma, Chunsheng
3 Milanič, Martin
3 Murty, Maruti Ram
3 Pintz, Janos
3 Richmond, L. Bruce
3 Södergren, Anders
3 Stankus, Eugenijus
3 Tan, Qianrong
3 Terras, Audrey Anne
3 Tripathi, Amitabha
2 Alon, Noga M.
2 Arenstorf, Richard F.
2 Audet, Charles
2 Balog, Antal
2 Bănescu, Magdalena
2 Bell, Jason P.
2 Berkovich, Alexander
2 Bertola, Marco
2 Bohman, Jan
2 Borwein, Peter Benjamin
2 Cilleruelo, Javier
2 Clark, Peter Louis
2 Compton, Kevin J.
2 Dai, Lixia
2 Duran, Mario M.
2 El-Sirafy, Ibrahim H.
2 Erdélyi, Tamás
2 Erdős, Pál
2 Farhi, Bakir
2 Fomenko, Oleg Mstislavovich
2 Fröberg, Carl-Erik
2 Fujima, Shoichi
2 Gallot, Yves
2 Granville, Andrew James
2 Hansen, Pierre
2 Hayashi, Elmer K.
2 Hirschhorn, Michael D.
2 Hofmeister, Gerd Rolf
2 Indlekofer, Karl-Heinz
2 Jiang, Yujiao
2 Kahane, Jean-Pierre
2 Kamiński, Marcin Marek
2 Kanemitsu, Shigeru
2 Laurinčikas, Antanas
2 Lu, Guangshi
2 McCurley, Kevin S.
2 Medvedev, Paul
2 Meir, Amram
2 Menzer, Hartmut
2 Messine, Frédéric
2 Montgomery, Hugh Lowell
2 Moree, Pieter
2 Moschella, Ugo
2 Müller, Helmut
2 Nédélec, Jean-Claude
2 Pan, Hao
2 Parhi, H. K.
2 Pollack, Paul
2 Polubarinova Kochina, Pelageya Yakovlevna
2 Popa, Dumitru
2 Rué, Juanjo
2 Šarka, Paulius
2 Satoh, Takakazu
2 Schaeffer, Richard
2 Schinzel, Andrzej
2 Scholl, Travis
2 Sós, Vera Turán
2 Soundararajan, Kannan
2 Suryanarayana, D.
2 Suzuki, Yuta
2 Tao, Terence
2 Thomas, Wolfgang
2 Turán, Pál
2 Udell, Gabe
2 Vorhauer, Ulrike Magdalena Anna
2 Washington, Lawrence C.
2 Watkins, Mark James
2 Ziegler, Tamar
2 Zumalacárregui, Ana
...and 441 more Authors
all top 5

Cited in 141 Serials

58 Journal of Number Theory
30 Mathematics of Computation
12 Mathematische Zeitschrift
12 Transactions of the American Mathematical Society
11 Archiv der Mathematik
11 Proceedings of the American Mathematical Society
11 International Journal of Number Theory
10 The Ramanujan Journal
9 Acta Arithmetica
9 Mathematische Annalen
9 Monatshefte für Mathematik
9 Journal de Théorie des Nombres de Bordeaux
6 Mathematika
5 Lithuanian Mathematical Journal
5 Periodica Mathematica Hungarica
5 Functiones et Approximatio. Commentarii Mathematici
5 Journal of Combinatorial Theory. Series A
5 Journal of Computational and Applied Mathematics
4 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
4 Advances in Mathematics
4 Acta Mathematica Hungarica
4 Experimental Mathematics
3 Acta Mechanica
3 Bulletin of the Australian Mathematical Society
3 Discrete Mathematics
3 International Journal of Engineering Science
3 Israel Journal of Mathematics
3 Journal of Mathematical Analysis and Applications
3 Mathematical Proceedings of the Cambridge Philosophical Society
3 Acta Mathematica
3 Compositio Mathematica
3 Inventiones Mathematicae
3 The Journal of Symbolic Logic
3 Indagationes Mathematicae. New Series
3 PMM, Journal of Applied Mathematics and Mechanics
2 Computers & Mathematics with Applications
2 Journal of Engineering Mathematics
2 Nuclear Physics. B
2 Rocky Mountain Journal of Mathematics
2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 Annali di Matematica Pura ed Applicata. Serie Quarta
2 Bulletin de la Société Mathématique de France
2 Duke Mathematical Journal
2 Journal of Algebra
2 Manuscripta Mathematica
2 Numerische Mathematik
2 Proceedings of the Japan Academy. Series A
2 Rendiconti del Circolo Matemàtico di Palermo. Serie II
2 Theoretical Computer Science
2 European Journal of Combinatorics
2 Journal of the American Mathematical Society
2 Mathematical and Computer Modelling
2 Journal of Cryptology
2 Designs, Codes and Cryptography
2 Bulletin of the American Mathematical Society. New Series
2 Acta Mathematica Sinica. New Series
2 Bulletin des Sciences Mathématiques
2 Journal of Integer Sequences
2 Annals of Mathematics. Second Series
2 Acta Mathematica Sinica. English Series
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Bulletin of the American Mathematical Society
2 BIT. Nordisk Tidskrift for Informationsbehandling
2 Forum of Mathematics, Pi
1 Advances in Applied Probability
1 American Mathematical Monthly
1 Communications in Mathematical Physics
1 Information Processing Letters
1 Journal d’Analyse Mathématique
1 Journal of Computational Physics
1 Journal of the Franklin Institute
1 Journal of Mathematical Biology
1 Journal of Mathematical Physics
1 Journal of Statistical Physics
1 Mathematical Notes
1 Mathematische Semesterberichte
1 Physics Letters. A
1 Reports on Mathematical Physics
1 The Mathematical Intelligencer
1 Annales de l’Institut Fourier
1 Annals of the Institute of Statistical Mathematics
1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
1 Archivum Mathematicum
1 BIT
1 Illinois Journal of Mathematics
1 International Journal of Mathematics and Mathematical Sciences
1 Journal of Applied Probability
1 Journal of Approximation Theory
1 Journal of Combinatorial Theory. Series B
1 Journal of Graph Theory
1 Journal of Optimization Theory and Applications
1 Journal of Soviet Mathematics
1 Journal of Statistical Planning and Inference
1 Mathematica Slovaca
1 Mechanics Research Communications
1 Osaka Journal of Mathematics
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Rendiconti del Seminario Matematico della Università di Padova
1 Semigroup Forum
1 Mathematical Social Sciences
...and 41 more Serials
all top 5

Cited in 48 Fields

311 Number theory (11-XX)
30 Combinatorics (05-XX)
15 Information and communication theory, circuits (94-XX)
12 Algebraic geometry (14-XX)
12 Probability theory and stochastic processes (60-XX)
11 Group theory and generalizations (20-XX)
10 Mathematical logic and foundations (03-XX)
9 Functions of a complex variable (30-XX)
9 Computer science (68-XX)
8 Commutative algebra (13-XX)
8 Special functions (33-XX)
8 Dynamical systems and ergodic theory (37-XX)
7 Partial differential equations (35-XX)
7 Convex and discrete geometry (52-XX)
7 Mechanics of deformable solids (74-XX)
6 Operator theory (47-XX)
6 Quantum theory (81-XX)
5 Numerical analysis (65-XX)
5 Fluid mechanics (76-XX)
4 Field theory and polynomials (12-XX)
4 Approximations and expansions (41-XX)
4 Statistics (62-XX)
4 Statistical mechanics, structure of matter (82-XX)
4 Operations research, mathematical programming (90-XX)
3 History and biography (01-XX)
3 Linear and multilinear algebra; matrix theory (15-XX)
3 Measure and integration (28-XX)
3 Potential theory (31-XX)
3 Sequences, series, summability (40-XX)
2 Harmonic analysis on Euclidean spaces (42-XX)
2 Integral transforms, operational calculus (44-XX)
2 Geometry (51-XX)
2 Relativity and gravitational theory (83-XX)
2 Mathematics education (97-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Topological groups, Lie groups (22-XX)
1 Real functions (26-XX)
1 Ordinary differential equations (34-XX)
1 Abstract harmonic analysis (43-XX)
1 Functional analysis (46-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 General topology (54-XX)
1 Mechanics of particles and systems (70-XX)
1 Optics, electromagnetic theory (78-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 Biology and other natural sciences (92-XX)
1 Systems theory; control (93-XX)

Citations by Year

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