Aldo Peretti

Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132

Volume 3, 1997, Number 2, Pages 75–101

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Aldo Peretti

*F**acultad de Ciencia y Tecnologla
Univcrsidad del Salvador
Cordoba 1739*

### References

- G. HARDY and J. E. LITTLEWOOD, Some problems in ‘Partitio Numerorum’ III, Acu Math. (1922), p. 1-70.
- A. PERETTI, The Goldbach problem (II). Notes on Numb. Theory and Discrete Math.. Vol. 2 (1996) N* 2. p. 1-26.
- L. K. HUA, Additive theory of prime numbers. Amer. Math. Soc. (1965). Ch. VH. p. 78.
- N. NORLUND, Vorlcsungen uber Differcrucnrcchnung. Chelsea Edition (1954).
- Y. LUKE. The special functions and their approximations. (1969) Academic Press. Vol. 1, {43. formula (3). p. 117.
- G. CARR, Formulas and theorems in Pure Mathematics, Chelsea Edition, p. 546-550.
- E. LANDAU, Vorlesungen Uber Zahlcntheorie. Chelsea Edition, Kap. I, { 1, formulas (266) and (267). More clear exposition in:

G. HARDY and J. E. LITTLEWOOD. Some problems of ‘Partitio Numerorum ’ (I). A neyv solution of Waring’s problem, GOtt. Nachr (1920), p. 33-54. - P. BATEMAN, On the representation of a number as the sum of 3 squares. Trans. Amer. Math. Soc. 71 (1951), p. 70-101.
- A. PERETTI, Euler’s diophantine equation x,‘ + … + x.k = i* . Bull. Numb. Theory. Vol. XU1 (1989), p. 39-50.
- H. MANN. A proof of the fundamental theorem on the density of sums of sets of positive integers. Aim. of Math. (2) 43 (1942). p. 523-527.
- B. KVARDA and R. K1LLGROVE, Extensions of the Schnirelman density to higher dimensions. Amer. Math. Monthly 73 (1966), p. 976-979.
- P. ERDOS, On the representation of large integers as sums of distinct summands taken from a fixed set. Acta Arith. 7 (1961/62), p. 345-354.
- G. LORENTZ. Multiplicity of representations of integers by sums of elements of two given sets, J. London Math. Soc. 28 (1953), 464-467.
- H. ROHRBACH. Ein Beitrag iur additiven Zahlcntheorie, Math. Z. (1937). 1-30. Zbl. 15.200.
- P. ERDOS and W. FUCHS, On a problem of additive number theory, J. London Math. Soc. 31 (1956), p. 67-73.
- A. PERETTI. The Fermat equation (II). Bull. Numb. Theory. Vol. XII (1988). p. 39-55.
- GRADSHTEIN-RYZIK, Table of Integrals. Series and Products, Academic Press (1965).
- N. NIELSEN. Handbuch der Theorie der Gamma Funktion. Chelsea Ed. (1965).

(19) G. HARDY and J. LITTLEWOOD, A new solution of Waring’s Problem, (P.N.I.) Quart. J. of Math. 48 (1919). p. 272-293.

(20) R. BAKHOOM, Asymptotic expansions of the function Fk (x) = I e *” du , Proceedings London Math. Soc. (2) (1933). p. 83-100.

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## Cite this paper

Peretti, A. (1997). Application of the Laplace transform to the solution of Diophantine equations. *Notes on Number Theory and Discrete Mathematics*, 3(2), 75-101.