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Title: ON A TWISTED VERSION OF LINNIK AND SELBERG'S CONJECTURE ON SUMS OF KLOOSTERMAN SUMS
Award ID(s):
1638352
PAR ID:
10175954
Author(s) / Creator(s):
Date Published:
Journal Name:
Mathematika
Volume:
65
Issue:
3
ISSN:
0025-5793
Page Range / eLocation ID:
437 to 474
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  1. We study three operations on Riordan arrays. First, we investigate when the sum of Riordan arrays yields another Riordan array. We characterize the A- and Z-sequences of these sums of Riordan arrays, and also identify an analog for A-sequences when the sum of Riordan arrays does not yield a Riordan array. In addition, we define the new operations `Der' and `Flip' on Riordan arrays. We fully characterize the Riordan arrays resulting from these operations applied to the Appell and Lagrange subgroups of the Riordan group. Finally, we study the application of these operations to various known Riordan arrays, generating many combinatorial identities in the process. 
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