selected publications
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book
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Analytic and elementary number theory.
Ed. 1.
1998
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Duality in Analytic Number Theory
1997
- Introduction to analytic number theory. Ed. 68. 1988
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Arithmetic Functions and Integer Products
1985
- Probabilistic number theory. II. Ed. 240. 1980
- Probabilistic number theory. I. Ed. 239. 1979
... more -
Analytic and elementary number theory.
Ed. 1.
1998
-
chapter
- Multiplicative Functions and the Sign of Maass Form Fourier Coefficients. 109-120. 2016
- AN ABSTRACT CENTRAL LIMIT THEOREM FOR EIGENFORMS. 131-142. 2012
- Elementary geometry of Hilbert spaces applied to abelian groups. 170-179. 2009
- The ramifications of a shift by 2. 69-77. 2007
- Product representations by rationals. 119-150. 2002
- The least prime primitive root and Linnik’s theorem. 393-418. 2002
- “Cast thy bread upon the waters$dots$” A personal view of the mathematician Paul ErdH os. 175-218. 2002
- On a multiplicative analogue of Goldbach’s conjecture. 771-793. 1999
- Shifted primes and Kubilius models. 297-312. 1997
- The distribution of the number of prime divisors of numbers of form $ab+1$. 313-321. 1997
- Fractional power large sieves. 323-332. 1996
- Applications of elementary functional analysis to the study of arithmetic functions. 35-43. 1990
- Multiplicative functions $vert gvert leq 1$ and their convolutions: an overview. 63-75. 1990
- Multiplicative functions on arithmetic progressions. III. The large moduli. 177-194. 1990
- Some remarks about multiplicative functions of modulus $leq 1$. 159-164. 1990
- Multiplicative functions on arithmetic progressions. 31-37. 1989
- The distribution of additive functions defined on short intervals. Exp. No. 29-8. 1988
- A new inequality in the theory of additive arithmetic functions. 53-58. 1983
- Subsequences of primes in residue classes to prime moduli. 157-164. 1983
- Recent results in the theory of arithmetic functions. 19-29. 1981
- On connections between the Turán-Kubilius inequality and the large sieve: some applications. 77-82. 1973
- The least prime in an arithmetic progression. 59-61. 1971
- A conjecture in prime number theory. 59-72. 1970
- Mean value theorems by the method of high moments. 31-34. 1970
... more -
conference proceeding
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journal article
- From Ramanujan to Groups of Rationals. A personal History of Abstract Multiplicative Functions. Springer Proceedings in Mathematics and Statistics. 267-295. 2018
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Multiplicative function mean values: asymptotic estimates.
Functiones et Approximatio Commentarii Mathematici.
2017
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HAEMONIC ANALYSIS ON THE POSITIVE RATIONALS. DETERMINATION OF THE GROUP GENERATED BY THE RATIOS (an plus b)/(An plus B).
Mathematika: a journal of pure and applied mathematics.
919-943.
2017
- Harmonic Analysis on the Positive Rationals I:Basic Results.. 569-614. 2016
- Harmonic Analysis on the Positive rationals II: Multiplicative Functions and Maass Forms. 615-658. 2016
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Additive and multiplicative functions from Nottingham to Urbana-Champaign.
International Journal of Number Theory.
1357-1366.
2015
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Central limit theorems for classical cusp forms.
The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu.
81-98.
2015
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Corrigendum: central limit theorems for classical cusp forms.
The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu.
99-102.
2015
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Jonas Kubilius and Probabilistic Number Theory Some Personal Reflections.
Lithuanian Mathematical Journal.
2-24.
2015
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A central limit theorem for Ramanujan's tau function.
The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu.
145-161.
2012
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Least zero of a cubic form.
Mathematische Annalen.
745-778.
2012
- The distribution in residue classes of integers omitting unspecified prime divisors. Commentarii Mathematici Universitatis Sancti Pauli. 9-14. 2011
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Variations on a Paper of Erdős and Heilbronn.
Canadian Mathematical Bulletin.
654-660.
2010
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The value distribution of additive arithmetic functions on a line.
Journal fuer die Reine und Angewandte Mathematik: Crelle's journal.
57-108.
2010
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Monotone additive functions on shifted primes.
The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu.
87-102.
2008
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Primes in progressions to moduli with a large power factor.
The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu.
241-251.
2007
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Primes and powers of a fixed integer, II.
Journal fuer die Reine und Angewandte Mathematik: Crelle's journal.
2004
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ON PRIMES AND POWERS OF A FIXED INTEGER.
Journal of London Mathematical Society.
365-379.
2003
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More primes and polynomials.
The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu.
299-320.
2003
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Primes, products and polynomials.
Inventiones Mathematicae.
453-487.
2002
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Multiplicative Functions on Arithmetic Progressions. VII: Large Moduli.
Journal of London Mathematical Society.
14-28.
2002
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Primes in short arithmetic progressions with rapidly increasing differences.
Transactions of the American Mathematical Society.
2705-2724.
2001
- Ramifications of probabilistic number theory. 33-50. 2001
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The multiplicative group of rationals generated by the shifted primes, II.
Journal fuer die Reine und Angewandte Mathematik: Crelle's journal.
2000
-
Product Bases for the Rationals.
Canadian Mathematical Bulletin.
441-444.
1999
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Products of shifted primes: Multiplicative analogues of Goldbach's problem.
Acta Arithmetica.
31-50.
1999
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The least primitive root mod 2; p; 2.
Mathematika: a journal of pure and applied mathematics.
371-379.
1998
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On products of shifted primes.
The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu.
219-223.
1998
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Products of shifted primes. Multiplicative analogues of Goldbach’s problems. II.
The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu.
201-217.
1998
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On the Average of the Least Primitive Root Modulo p.
Journal of London Mathematical Society.
435-454.
1997
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The multiplicative group of rationals generated by the shifted primes, I..
Journal fuer die Reine und Angewandte Mathematik: Crelle's journal.
169-216.
1995
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On the correlation of multiplicative and the sum of additive arithmetic functions.
Memoirs of the American Mathematical Society.
0-0.
1994
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The concentration function of additive functions on shifted primes.
Acta Mathematica.
1-35.
1994
- The multiplicative group of rationals generated by the shifted primes. 1-9. 1994
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From a Large Sieve to the Orthogonality of Operators.
Journal of London Mathematical Society.
427-440.
1993
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Multiplicative Functions on Arithmetic Progressions. VI. More Middle Moduli.
Journal of Number Theory.
178-208.
1993
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Additive functions on shifted primes.
Bulletin of the American Mathematical Society.
273-278.
1992
- On maximal versions of the large sieve. II. 379-383. 1992
- On the correlation of multiplicative functions. 1-11. 1992
- On maximal versions of the large sieve. 149-164. 1991
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Multiplicative Functions on Arithmetic Progressions: V. Composite Moduli.
Journal of London Mathematical Society.
408-424.
1990
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Multiplicative Functions on Arithmetic Progressions: IV. The Middle Moduli.
Journal of London Mathematical Society.
201-216.
1990
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The value distribution of differences of additive arithmetic functions.
Journal of Number Theory.
339-370.
1989
- Extrapolating the mean-values of multiplicative functions. Indagationes Mathematicae. 409-420. 1989
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A localized Erdős-Wintner theorem.
Pacific Journal of Mathematics.
287-297.
1988
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Multiplicative functions on arithmetic progressions, II..
Mathematika: a journal of pure and applied mathematics.
38-50.
1988
-
The distribution of the number of prime divisors of sums a + b.
Journal of Number Theory.
94-99.
1988
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Additive arithmetic functions on intervals.
Cambridge Philosophical Society: Mathematical Proceedings.
163-179.
1988
-
Multiplicative functions on arithmetic progressions.
Mathematika: a journal of pure and applied mathematics.
199-206.
1987
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The Norms of Compositions of Arithmetic Operators.
Bulletin of the London Mathematical Society.
522-530.
1987
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Localised value-distribution of additive arithmetic functions..
Journal fuer die Reine und Angewandte Mathematik: Crelle's journal.
64-75.
1987
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A local Turán-Kubilius inequality.
Acta Arithmetica.
127-139.
1987
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Additive Arithmetic Functions on Arithmetic Progressions.
Proceedings of the London Mathematical Society.
15-37.
1987
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Functional analysis and additive arithmetic functions.
Bulletin of the American Mathematical Society.
179-223.
1987
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Persistence of Form and the Value Group of Reducible Cubics.
Transactions of the American Mathematical Society.
133-133.
1987
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On the multiplicative group generated by a dense sequence of integers.
Monatshefte fuer Mathematik.
3-6.
1986
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Linear Recurrences in Modules.
Bulletin of the London Mathematical Society.
1-4.
1986
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The Value Distribution of Reducible Cubics.
Canadian Mathematical Bulletin.
328-336.
1985
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An arithmetic operator and the functions on which it is part-bounded.
Letters in Mathematical Physics.
107-110.
1985
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On the absolute value of Ramanujan's ?-function.
Mathematische Annalen.
507-511.
1984
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On representing integers as products of thep + 1.
Monatshefte fuer Mathematik.
85-97.
1984
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Cauchy's functional equation in the mean.
Advances in Mathematics.
253-257.
1984
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On additive arithmetic functions f(n) for which f(an + b) − f(cn + d) is bounded.
Journal of Number Theory.
285-310.
1983
-
On the distribution of the roots of certain congruences and a problem for additive arithmetic functions.
Journal of Number Theory.
267-282.
1983
- On representing integers as products of integers of a prescribed type. Journal- Australian Mathematical Society Series a. 143-161. 1983
- The simultaneous representation of integers by products of certain rational functions. Journal- Australian Mathematical Society Series a. 405-420. 1983
- The exponential function characterized by an approximate functional equation. Illinois Journal of Mathematics. 503-518. 1982
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A remark on the Dirichlet values of a completely reducible polynomial (mod q).
Journal of Number Theory.
12-17.
1981
- Multiplicative functions and Ramanujan’s $τ $-function. Journal- Australian Mathematical Society Series a. 461-468. 1981
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On Sums of an Additive Arithmetic Function with Shifted Arguments.
Journal of London Mathematical Society.
25-38.
1980
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High-Power Analogues of the Turán-Kubilius Inequality, and an Application to Number Theory.
Canadian Journal of Mathematics.
893-907.
1980
- Mean value theorems for multiplicative functions bounded in mean $α $-power, $α >1$. Journal- Australian Mathematical Society Series a. 177-205. 1980
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On the differences of additive functions, II.
Acta Arithmetica.
249-256.
1980
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The tails of infinitely divisible laws and a problem in number theory.
Journal of Number Theory.
542-551.
1979
-
Sums and differences of additive arithmetic functions in mean square..
Journal fuer die Reine und Angewandte Mathematik: Crelle's journal.
21-54.
1979
- Additive arithmetic functions bounded by monotone functions on thin sets. 97-111. 1979
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On certain asymptotic functional equations.
Aequationes Mathematicae.
44-52.
1978
- On the differences of additive arithmetic functions. Mathematika: a journal of pure and applied mathematics. 153-165. 1977
- The Turán-Kubilius inequality. Proceedings of the American Mathematical Society. 8-10. 1977
- General asymptotic distributions for additive arithmetic functions. Cambridge Philosophical Society: Mathematical Proceedings. 43-54. 1976
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On a conjecture of Narkiewicz about functions with non-decreasing normal order.
Colloquium Mathematicum.
289-294.
1976
- On a problem of Hardy and Ramanujan. Mathematika: a journal of pure and applied mathematics. 10-17. 1976
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On two conjectures of Kátai.
Acta Arithmetica.
341-365.
1976
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A Mean-Value Theorem for Multiplicative Functions.
Proceedings of the London Mathematical Society.
418-438.
1975
-
On the Limiting Distribution of Additive Arithmetic Functions: Logarithmic Renormalization.
Proceedings of the London Mathematical Society.
364-384.
1975
- The law of large numbers for additive arithmetic functions. Cambridge Philosophical Society: Mathematical Proceedings. 33-71. 1975
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On the position of a theorem of Kubilius in probabilistic number theory.
Mathematische Annalen.
201-209.
1974
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A conjecture of Kátai.
Acta Arithmetica.
11-20.
1974
- On the limiting distribution of $f(p+1)$ for non-negative additive functions. Acta Arithmetica. 258-264. 1974
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On the limiting distribution of additive arithmetic functions.
Acta Mathematica.
53-75.
1974
- Sur les fonctions arithmétiques additives. 1573-1575. 1974
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On the distribution of the values of quadraticL-series in the half-plane ?>1/2.
Inventiones Mathematicae.
319-338.
1973
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On additive functions whose limiting distributions possess a finite mean and variance.
Pacific Journal of Mathematics.
47-55.
1973
- A class of additive arithmetic functions with asymptotically normal distribution. Mathematika: a journal of pure and applied mathematics. 144-154. 1973
- On distribution functions ($rm mod 1$): Quantitative Fourier inversion. Journal of Number Theory. 509-522. 1972
- On the distribution of $rm argL(s,,χ )$ in the half-plane $σ >1øver 2$. Acta Arithmetica. 155-169. 1972
- The Riemann zeta function and coin tossing. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal. 100-109. 1972
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On the limiting distribution of additive functions (mod 1).
Pacific Journal of Mathematics.
49-59.
1971
-
The Least Prime K; -th-Power Residue.
Journal of London Mathematical Society.
205-210.
1971
- On inequalities of large sieve type. Acta Arithmetica. 405-422. 1971
- On the distribution of the values of Dirichlet $L$-series in the half-plane $σ >1øver 2$. 222-234. 1971
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The distribution of the values of additive arithmetical functions.
Acta Mathematica.
143-164.
1971
-
On the Mean Value of f; (p; ).
Proceedings of the London Mathematical Society.
28-96.
1970
- Some applications of a theorem of Raikov to number theory. Journal of Number Theory. 22-55. 1970
- The Turan-Kubilius inequality, and a limitation theorem for the large sieve. American Journal of Mathematics. 293-300. 1970
-
The distribution of power residues and certain related results.
Acta Arithmetica.
141-159.
1970
- The distribution of the quadratic class number. Lietuvos Matematikos Rinkinys. 189-197. 1970
-
A Restricted Mean Value Theorem.
Journal of London Mathematical Society.
447-460.
1969
- A conjecture of Erdös concerning character sums. 164-171. 1969
- On the size of $L(1,,χ )$. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal. 26-36. 1969
- The distribution of primitive roots. Canadian Journal of Mathematics. 822-841. 1969
- Corrigendum: “A problem of Erdös concerning power residue sums”. Acta Arithmetica. 437-437. 1968
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On certain additive functions (II).
Acta Arithmetica.
51-64.
1968
- Some matching theorems. 215-219 (1969). 1968
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Some notes on k-th power residues.
Acta Arithmetica.
153-162.
1968
- The average of the least primitive root. Mathematika: a journal of pure and applied mathematics. 39-50. 1968
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On the number of circles determined byn points.
Acta Mathematica Hungarica.
181-188.
1967
-
A note on a recent paper of U. V. Linnik and A. I. Vinogradov.
Acta Arithmetica.
103-105.
1967
-
A problem of Erdös concerning power residue sums..
Acta Arithmetica.
131-149.
1967
-
On certain additive functions.
Acta Arithmetica.
365-384.
1967
- Mappings of finite sets. Mathematika: a journal of pure and applied mathematics. 23-25. 1966
- Some applications of Bombieri’s theorem. Mathematika: a journal of pure and applied mathematics. 196-203. 1966
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ON SEQUENCES OF INTEGERS.
Quarterly Journal of Mathematics.
35-45.
1965
... more