On the High-Indices Theorem for Borel Summability

A. E. Ingham

A chapter in Number Theory and Analysis, 1969, pp 119-135 from Springer

Abstract: Abstract In a volume dedicated to the memory of Landau, summability of series is an appropriate topic, for Landau was intensely interested in this subject and made important contributions to it. In particular, it was he who introduced the notion of one-sided Tauberian condition, thereby enriching the theory itself and opening the way to arithmetical applications. No such conditions will indeed appear in this paper, for we shall be concerned exclusively with a theorem of the ‘high-indices’ or ‘gap’ type, and it is characteristic of such theorems, in their most perfect forms, that they involve no explicit order condition (one-sided or two-sided) on the terms of the series.

Date: 1969
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DOI: 10.1007/978-1-4615-4819-5_9

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