## Arithmetic properties of Bernoulli convolutions

HTML articles powered by AMS MathViewer

- by Adriano M. Garsia PDF
- Trans. Amer. Math. Soc.
**102**(1962), 409-432 Request permission

## References

- Paul Erdös,
*On a family of symmetric Bernoulli convolutions*, Amer. J. Math.**61**(1939), 974–976. MR**311**, DOI 10.2307/2371641 - Paul Erdös,
*On the smoothness properties of a family of Bernoulli convolutions*, Amer. J. Math.**62**(1940), 180–186. MR**858**, DOI 10.2307/2371446
A. Garsia, - Børge Jessen and Aurel Wintner,
*Distribution functions and the Riemann zeta function*, Trans. Amer. Math. Soc.**38**(1935), no. 1, 48–88. MR**1501802**, DOI 10.1090/S0002-9947-1935-1501802-5 - J.-P. Kahane and R. Salem,
*Sur la convolution d’une infinité de distributions de Bernoulli*, Colloq. Math.**6**(1958), 193–202 (French). MR**101992**, DOI 10.4064/cm-6-1-193-202 - Samuel Karlin,
*Some random walks arising in learning models. I*, Pacific J. Math.**3**(1953), 725–756. MR**58910** - John G. Kemeny and J. Laurie Snell,
*Markov processes in learning theory*, Psychometrika**22**(1957), 221–230. MR**91234**, DOI 10.1007/BF02289123 - Richard Kershner and Aurel Wintner,
*On Symmetric Bernoulli Convolutions*, Amer. J. Math.**57**(1935), no. 3, 541–548. MR**1507093**, DOI 10.2307/2371185
C. Pisot, - J. Dufresnoy and Ch. Pisot,
*Sur un ensemble fermé d’entiers algébriques*, Ann. Sci. Ecole Norm. Sup. (3)**70**(1953), 105–133 (French). MR**0059956** - Marthe Hugot and Charles Pisot,
*Sur certains entiers algébriques*, C. R. Acad. Sci. Paris**246**(1958), 2831–2833 (French). MR**99322**
S. O. Rice, - R. Salem,
*A remarkable class of algebraic integers. Proof of a conjecture of Vijayaraghavan*, Duke Math. J.**11**(1944), 103–108. MR**10149** - Carl Ludwig Siegel,
*Algebraic integers whose conjugates lie in the unit circle*, Duke Math. J.**11**(1944), 597–602. MR**10579**

*On the distribution function of a geometric series whose terms have random changes of sign*, Bell Telephone Laboratories Technical Memorandum File, 1959.

*La répartition modulo un et les nombres algébriques*, Ann. Scuola Norm. Sup. Pisa

**2**(1938), 205-248.

*Statistical properties of the response of a resonant circuit to a train of random pulses*, Bell Telephone Laboratories Technical Memorandum File 36676-6.

## Additional Information

- © Copyright 1962 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**102**(1962), 409-432 - MSC: Primary 44.25
- DOI: https://doi.org/10.1090/S0002-9947-1962-0137961-5
- MathSciNet review: 0137961