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15 February 2009 A sieve method for shifted convolution sums
Roman Holowinsky
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Duke Math. J. 146(3): 401-448 (15 February 2009). DOI: 10.1215/00127094-2009-002

Abstract

We study the average size of shifted convolution summation terms related to the problem of quantum unique ergodicity (QUE) on SL2(Z)\H. Establishing an upper-bound sieve method for handling such sums, we achieve an unconditional result that suggests that the average size of the summation terms should be sufficient in application to quantum unique ergodicity. In other words, cancellations among the summation terms, although welcomed, may not be required. Furthermore, the sieve method may be applied to shifted sums of other multiplicative functions with similar results under suitable conditions

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Roman Holowinsky. "A sieve method for shifted convolution sums." Duke Math. J. 146 (3) 401 - 448, 15 February 2009. https://doi.org/10.1215/00127094-2009-002

Information

Published: 15 February 2009
First available in Project Euclid: 14 January 2009

zbMATH: 1218.11089
MathSciNet: MR2484279
Digital Object Identifier: 10.1215/00127094-2009-002

Subjects:
Primary: 11F30 , 11N36
Secondary: 11M99

Rights: Copyright © 2009 Duke University Press

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Vol.146 • No. 3 • 15 February 2009
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