Lacunary function - Open Access .click

Russian Mathematical Surveys, 1966
CONTENTSIntroductionChapter I. Lacunary subsystems of general systems of functions § 1. Definitions and notation § 2. Convergence § 3. Integrability § 4. Absolute convergence § 5. The central limit theorem § 6. The law of the iterated logarithmChapter II. Lacunary subsystems of specific systems of functions § 1. The trigonometric system § 2.
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Lacunary partition functions

Mathematical Research Letters, 2002
A function \(f(q)\) is lacunary if \(f(q)= \sum_{n\geq 0} a(n)q^n\) and \(a(n)\) is almost always \(0\). It is known by the work of J.-P. Serre, B. Gordon and S. Robins that there are approximately 60 pairs \((r,s)\) for which \[ \prod_{n=1}^\infty (1-q^n)^r(1-q^{2n})^s \] is lacunary.
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Lacunary entire functions

Mathematical Proceedings of the Cambridge Philosophical Society, 1993
AbstractIt has been observed that lacunary functions and random functions often have many properties in common (cf. [5]). The present paper has the object of showing that lacunary entire functions behave in many respects like random entire functions. Both have the property of being large except in very small neighbourhoods of their zeros and these have
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