# zbMATH — the first resource for mathematics

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 Documents Indexed: 70 Publications since 1980, including 7 Books Reviewing Activity: 155 Reviews
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#### Co-Authors

 45 single-authored 7 Berndt, Bruce Carl 7 Diamond, Harold George 5 Tenenbaum, Gérald 4 Bennett, Michael A. 4 Boston, Nigel 4 Philipp, Walter 3 Li, Junxian 3 Maier, Helmut 2 Cai, Zhaodong 2 Spilker, Jürgen 1 Bateman, Paul Trevier 1 Deutsch, Emeric 1 Erdős, Pál 1 Faust, Matthew 1 Friedlander, John Benjamin 1 Granville, Andrew James 1 Halberstam, Heini 1 He, Xinwei 1 Li, Xiaomin 1 Li, Yuchen 1 Odlyzko, Andrew M. 1 Phillips, Reed 1 Pudaite, P. 1 Purdy, George B. 1 Reznick, Bruce 1 Schwarz, Wolfgang Karl 1 Wilf, Herbert S. 1 Xie, Yun 1 Zhang, Yuan 1 Zhang, Yunyi
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#### Serials

 4 Journal of the London Mathematical Society. Second Series 3 Acta Arithmetica 3 Journal of Number Theory 3 Mathematika 3 Proceedings of the American Mathematical Society 3 Transactions of the American Mathematical Society 3 Progress in Mathematics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Michigan Mathematical Journal 2 Monatshefte für Mathematik 2 Pacific Journal of Mathematics 1 American Mathematical Monthly 1 Journal d’Analyse Mathématique 1 Annales de l’Institut Fourier 1 The Annals of Probability 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Compositio Mathematica 1 Duke Mathematical Journal 1 Journal für die Reine und Angewandte Mathematik 1 Manuscripta Mathematica 1 Mathematische Zeitschrift 1 Proceedings of the London Mathematical Society. Third Series 1 The Quarterly Journal of Mathematics. Oxford Second Series 1 Comptes Rendus Mathématiques de l’Académie des Sciences 1 Probability Theory and Related Fields 1 Journal of the American Mathematical Society 1 Aequationes Mathematicae 1 L’Enseignement Mathématique. 2e Série 1 Journal de Théorie des Nombres de Bordeaux 1 The Electronic Journal of Combinatorics 1 Discrete Mathematics and Theoretical Computer Science. DMTCS 1 RIMS Kokyuroku 1 Journal of Integer Sequences 1 Integers 1 International Journal of Number Theory 1 Publications Mathématiques d’Orsay
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#### Fields

 68 Number theory (11-XX) 7 General and overarching topics; collections (00-XX) 4 Probability theory and stochastic processes (60-XX) 3 Combinatorics (05-XX) 2 Ordinary differential equations (34-XX) 1 Sequences, series, summability (40-XX) 1 Integral equations (45-XX)

#### Citations contained in zbMATH Open

48 Publications have been cited 469 times in 327 Documents Cited by Year
Integers without large prime factors. Zbl 0797.11070
1993
On the number of positive integers $$\leq x$$ and free of prime factors $$>y$$. Zbl 0575.10038
1986
On integers free of large prime factors. Zbl 0601.10028
1986
On the number of prime factors of an integer. Zbl 0655.10036
1988
The asymptotic behavior of the solutions of a class of differential- difference equations. Zbl 0675.34037
1990
On a class of differential-difference equations arising in number theory. Zbl 0797.11072
1993
An Erdős-Wintner theorem for differences of additive functions. Zbl 0707.11057
1988
Integers free of large prime divisors in short intervals. Zbl 0562.10018
1985
Integers free of large prime factors and the Riemann Hypothesis. Zbl 0544.10042
1984
On a conjecture of Balog. Zbl 0597.10056
1985
On the pointwise convergence of Ramanujan expansions of number-theoretic functions. Zbl 0507.10001
1984
On consecutive values of the Liouville function. Zbl 0615.10054
1986
1980
Longest increasing subsequences in pattern-restricted permutations. Zbl 1011.05008
Deutsch, Emeric; Hildebrand, A. J.; Wilf, Herbert S.
2003
Oscillation theorems for primes in arithmetic progressions and for sifting functions. Zbl 0724.11040
Friedlander, John; Granville, Andrew; Hildebrand, Adolf; Maier, Helmut
1991
On the local behavior of $$\Psi$$ (x,y). Zbl 0611.10028
1986
Additive and multiplicative functions on shifted primes. Zbl 0644.10034
1989
Large values of character sums. Zbl 0652.10029
1988
On the number of prime factors of integers without large prime divisors. Zbl 0621.10028
1987
A note on Burgess’ character sum estimate. Zbl 0589.10039
1986
Irregularities in the distribution of primes in short intervals. Zbl 0658.10048
1989
On the constant in the Polya-Vinogradov inequality. Zbl 0612.10033
1988
Multiplicative functions at consecutive integers. Zbl 0615.10053
1986
An asymptotic formula for the variance of an additive function. Zbl 0493.10049
1983
Multiplicative functions on arithmetic progressions. Zbl 0692.10038
1990
Multiplicative functions in short intervals. Zbl 0618.10040
1987
The divisor function at consecutive integers. Zbl 0591.10035
1987
The asymptotic behavior of a family of sequences. Zbl 0558.10010
Erdős, Paul; Hildebrand, A.; Odlyzko, Andrew M.; Pudaite, P.; Reznick, B.
1987
The prime number theorem via the large sieve. Zbl 0575.10036
1986
Quantitative mean value theorems for nonnegative multiplicative functions. I. Zbl 0573.10033
1985
Erdős’ problems on consecutive integers. Zbl 1046.11071
Hildebrand, A. J.
2002
On integer sets containing strings of consecutive integers. Zbl 0685.10036
1989
Multiplicative functions at consecutive integers. II. Zbl 0663.10047
1988
Gaps between prime numbers. Zbl 0663.10046
1988
On the limit distribution of discrete random variables. Zbl 0594.60050
1987
Quantitative mean value theorems for nonnegative multiplicative functions. II. Zbl 0573.10034
1987
On Wirsing’s mean value theorem for multiplicative functions. Zbl 0564.10048
1986
Sur les moments d’une fonction additive. Zbl 0486.10043
1983
A note on the convergence of sums of independent random variables. Zbl 0762.60019
1992
On consecutive $$k$$th power residues. II. Zbl 0727.11036
1991
On consecutive k-th power residues. Zbl 0593.10037
1986
A local Benford law for a class of arithmetic sequences. Zbl 1445.11079
Cai, Zhaodong; Hildebrand, A. J.; Li, Junxian
2019
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
Bennett, M. A. (ed.); Berndt, B. C. (ed.); Boston, N. (ed.); Diamond, H. G. (ed.); Hildebrand, A. J. (ed.); Philipp, W. (ed.)
2002
Sums of distinct squares. Zbl 0815.11048
Bateman, Paul T.; Hildebrand, Adolf J.; Purdy, George B.
1994
On some Tauberian theorems related to the prime number theorem. Zbl 0804.11052
Hildebrand, A.; Tenenbaum, G.
1994
On the least pair of consecutive quadratic non-residues. Zbl 0617.10002
1987
Additive functions on arithmetic progressions. Zbl 0573.10032
1986
On a problem of Erdős and Alladi. Zbl 0531.10046
1984
A local Benford law for a class of arithmetic sequences. Zbl 1445.11079
Cai, Zhaodong; Hildebrand, A. J.; Li, Junxian
2019
Longest increasing subsequences in pattern-restricted permutations. Zbl 1011.05008
Deutsch, Emeric; Hildebrand, A. J.; Wilf, Herbert S.
2003
Erdős’ problems on consecutive integers. Zbl 1046.11071
Hildebrand, A. J.
2002
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
Bennett, M. A. (ed.); Berndt, B. C. (ed.); Boston, N. (ed.); Diamond, H. G. (ed.); Hildebrand, A. J. (ed.); Philipp, W. (ed.)
2002
Sums of distinct squares. Zbl 0815.11048
Bateman, Paul T.; Hildebrand, Adolf J.; Purdy, George B.
1994
On some Tauberian theorems related to the prime number theorem. Zbl 0804.11052
Hildebrand, A.; Tenenbaum, G.
1994
Integers without large prime factors. Zbl 0797.11070
1993
On a class of differential-difference equations arising in number theory. Zbl 0797.11072
1993
A note on the convergence of sums of independent random variables. Zbl 0762.60019
1992
Oscillation theorems for primes in arithmetic progressions and for sifting functions. Zbl 0724.11040
Friedlander, John; Granville, Andrew; Hildebrand, Adolf; Maier, Helmut
1991
On consecutive $$k$$th power residues. II. Zbl 0727.11036
1991
The asymptotic behavior of the solutions of a class of differential- difference equations. Zbl 0675.34037
1990
Multiplicative functions on arithmetic progressions. Zbl 0692.10038
1990
Additive and multiplicative functions on shifted primes. Zbl 0644.10034
1989
Irregularities in the distribution of primes in short intervals. Zbl 0658.10048
1989
On integer sets containing strings of consecutive integers. Zbl 0685.10036
1989
On the number of prime factors of an integer. Zbl 0655.10036
1988
An Erdős-Wintner theorem for differences of additive functions. Zbl 0707.11057
1988
Large values of character sums. Zbl 0652.10029
1988
On the constant in the Polya-Vinogradov inequality. Zbl 0612.10033
1988
Multiplicative functions at consecutive integers. II. Zbl 0663.10047
1988
Gaps between prime numbers. Zbl 0663.10046
1988
On the number of prime factors of integers without large prime divisors. Zbl 0621.10028
1987
Multiplicative functions in short intervals. Zbl 0618.10040
1987
The divisor function at consecutive integers. Zbl 0591.10035
1987
The asymptotic behavior of a family of sequences. Zbl 0558.10010
Erdős, Paul; Hildebrand, A.; Odlyzko, Andrew M.; Pudaite, P.; Reznick, B.
1987
On the limit distribution of discrete random variables. Zbl 0594.60050
1987
Quantitative mean value theorems for nonnegative multiplicative functions. II. Zbl 0573.10034
1987
On the least pair of consecutive quadratic non-residues. Zbl 0617.10002
1987
On the number of positive integers $$\leq x$$ and free of prime factors $$>y$$. Zbl 0575.10038
1986
On integers free of large prime factors. Zbl 0601.10028
1986
On consecutive values of the Liouville function. Zbl 0615.10054
1986
On the local behavior of $$\Psi$$ (x,y). Zbl 0611.10028
1986
A note on Burgess’ character sum estimate. Zbl 0589.10039
1986
Multiplicative functions at consecutive integers. Zbl 0615.10053
1986
The prime number theorem via the large sieve. Zbl 0575.10036
1986
On Wirsing’s mean value theorem for multiplicative functions. Zbl 0564.10048
1986
On consecutive k-th power residues. Zbl 0593.10037
1986
Additive functions on arithmetic progressions. Zbl 0573.10032
1986
Integers free of large prime divisors in short intervals. Zbl 0562.10018
1985
On a conjecture of Balog. Zbl 0597.10056
1985
Quantitative mean value theorems for nonnegative multiplicative functions. I. Zbl 0573.10033
1985
Integers free of large prime factors and the Riemann Hypothesis. Zbl 0544.10042
1984
On the pointwise convergence of Ramanujan expansions of number-theoretic functions. Zbl 0507.10001
1984
On a problem of Erdős and Alladi. Zbl 0531.10046
1984
An asymptotic formula for the variance of an additive function. Zbl 0493.10049
1983
Sur les moments d’une fonction additive. Zbl 0486.10043
1983
1980
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#### Cited by 303 Authors

 20 Tenenbaum, Gérald 16 Shparlinski, Igor E. 12 Granville, Andrew James 12 Hildebrand, Adolf J. 11 Banks, William D. 9 Luca, Florian 7 de la Bretèche, Régis 7 Friedlander, John Benjamin 7 Manstavičius, Eugenijus 7 Soundararajan, Kannan 7 Stepanauskas, Gediminas 6 De Koninck, Jean-Marie 6 Drappeau, Sary 6 Indlekofer, Karl-Heinz 6 Kátai, Imre 6 Konyagin, Sergeĭ Vladimirovich 6 Maier, Helmut 6 Tao, Terence 5 Ford, Kevin B. 5 Goldston, Daniel Alan 5 Harman, Glyn 5 Hwang, Hsien-Kuei 5 Lucht, Lutz Gerhard 5 Pomerance, Carl Bernard 4 Elliott, Peter D. T. A. 4 Moree, Pieter 4 Pintz, Janos 4 Sankaranarayanan, Ayyadurai 4 Šiaulys, Jonas 4 Wu, Jie 3 Alkan, Emre 3 Balazard, Michel 3 Hall, Richard R. 3 Harper, Adam J. 3 Kerr, Bryce 3 Lagarias, Jeffrey C. 3 Mansour, Toufik 3 Matomäki, Kaisa Sofia 3 Murty, Maruti Ram 3 Saha, Biswajyoti 3 Shao, Xuancheng 3 Teräväinen, Joni 3 Wang, Zhiwei 3 Warlimont, Richard 3 Zaharescu, Alexandru 2 Akbal, Yıldırım 2 Arratia, Richard Alejandro 2 Asci, Claudio 2 Bachman, Gennady 2 Bai, Shi 2 Balog, Antal 2 Bourgain, Jean 2 Elsholtz, Christian 2 Freiberg, Tristan 2 Giuliano, Rita 2 Goldmakher, Leo 2 Jonasson, Johan 2 Kan, Jiahai 2 Kim, Sungjin 2 Klurman, Oleksiy 2 Liu, Jianya 2 Martin, Bruno 2 Mauduit, Christian 2 McCurley, Kevin S. 2 Mehdizadeh, Marzieh 2 Montgomery, Hugh Lowell 2 Munsch, Marc 2 Pak, Igor 2 Petuchovas, Robertas 2 Phong, Biu Minh 2 Shan, Zun 2 Shteĭnikov, Yuriĭ Nikolaevich 2 Sorenson, Jonathan P. 2 Stewart, Cameron L. 2 Suzuki, Koji 2 Timofeev, Nikolaĭ Mikhaĭlovich 2 Usmanov, Kh. Kh. 2 Xuan, Tizuo 2 Yıldırım, Gökhan 2 Žvinytė, Laura 1 Aguech, Rafik 1 Amri, Anis 1 Angel, Omer 1 Avdeeva, M. O. 1 Bach, Eric 1 Baker, Roger C. 1 Balasubramanian, Ramachandran 1 Balasuriya, Sanka 1 Balister, Paul N. 1 Barbour, Andrew D. 1 Barbulescu, Razvan 1 Basquin, Joseph 1 Baxendale, Peter H. 1 Bernstein, Daniel Julius 1 Bhagvati, Chakravarthy 1 Bhowmick, Abhishek 1 Bingham, Nicholas Hugh 1 Birkner, Peter 1 Bisson, Gaetan 1 Blomer, Valentin ...and 203 more Authors
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#### Cited in 104 Serials

 39 Journal of Number Theory 14 The Ramanujan Journal 11 Mathematics of Computation 11 Mathematika 10 Lithuanian Mathematical Journal 9 Functiones et Approximatio. Commentarii Mathematici 9 Proceedings of the American Mathematical Society 9 International Journal of Number Theory 8 Transactions of the American Mathematical Society 7 Acta Mathematica Hungarica 6 Archiv der Mathematik 6 Monatshefte für Mathematik 6 Indagationes Mathematicae. New Series 6 Journal de Théorie des Nombres de Bordeaux 5 Compositio Mathematica 5 Manuscripta Mathematica 5 Michigan Mathematical Journal 5 Journal of the American Mathematical Society 4 Bulletin of the Australian Mathematical Society 4 Journal d’Analyse Mathématique 4 Mathematical Notes 4 Acta Arithmetica 4 Duke Mathematical Journal 4 Journal of Combinatorial Theory. Series A 4 Mathematische Annalen 4 Theoretical Computer Science 4 The Annals of Applied Probability 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Proceedings of the Steklov Institute of Mathematics 3 Annales de l’Institut Fourier 3 Journal für die Reine und Angewandte Mathematik 3 Mathematische Zeitschrift 3 Journal of Theoretical Probability 3 Annals of Mathematics. Second Series 3 Integers 3 Science China. Mathematics 2 Discrete Mathematics 2 Information Processing Letters 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Rocky Mountain Journal of Mathematics 2 Acta Mathematica 2 Advances in Mathematics 2 Advances in Applied Mathematics 2 Acta Applicandae Mathematicae 2 Forum Mathematicum 2 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série 2 Bulletin of the American Mathematical Society. New Series 2 Experimental Mathematics 2 Chebyshevskiĭ Sbornik 2 Forum of Mathematics, Sigma 2 Annales Mathématiques du Québec 1 International Journal of Modern Physics B 1 Discrete Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Moscow University Mathematics Bulletin 1 Periodica Mathematica Hungarica 1 Russian Mathematical Surveys 1 The Mathematical Intelligencer 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 The Annals of Probability 1 Bulletin of the London Mathematical Society 1 Bulletin de la Société Mathématique de France 1 Canadian Mathematical Bulletin 1 Colloquium Mathematicum 1 Illinois Journal of Mathematics 1 Inventiones Mathematicae 1 Journal of Computational and Applied Mathematics 1 Journal of Functional Analysis 1 Mathematische Nachrichten 1 Mathematica Slovaca 1 Osaka Journal of Mathematics 1 Quaestiones Mathematicae 1 European Journal of Combinatorics 1 Statistics & Probability Letters 1 Stochastic Analysis and Applications 1 Applied Numerical Mathematics 1 Probability Theory and Related Fields 1 Random Structures & Algorithms 1 Geometric and Functional Analysis. GAFA 1 Aequationes Mathematicae 1 Linear Algebra and its Applications 1 The Australasian Journal of Combinatorics 1 Theory of Probability and Mathematical Statistics 1 Turkish Journal of Mathematics 1 Finite Fields and their Applications 1 Electronic Journal of Probability 1 Electronic Research Announcements of the American Mathematical Society 1 Doklady Mathematics 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Discrete Mathematics and Theoretical Computer Science. DMTCS 1 Journal of Discrete Mathematical Sciences & Cryptography 1 Journal of Integer Sequences 1 Journal of the European Mathematical Society (JEMS) 1 Acta Mathematica Sinica. English Series 1 RAIRO. Theoretical Informatics and Applications 1 Lobachevskii Journal of Mathematics 1 Journal of the Australian Mathematical Society 1 Algebra & Number Theory 1 European Journal of Pure and Applied Mathematics 1 Bulletin of Mathematical Sciences ...and 4 more Serials
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#### Cited in 24 Fields

 291 Number theory (11-XX) 28 Probability theory and stochastic processes (60-XX) 21 Combinatorics (05-XX) 8 Computer science (68-XX) 7 Ordinary differential equations (34-XX) 6 History and biography (01-XX) 5 Functions of a complex variable (30-XX) 5 Numerical analysis (65-XX) 4 Group theory and generalizations (20-XX) 4 Information and communication theory, circuits (94-XX) 3 Algebraic geometry (14-XX) 3 Statistics (62-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Sequences, series, summability (40-XX) 2 Integral transforms, operational calculus (44-XX) 2 Operator theory (47-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX)