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Telescopers for differential forms with one parameter

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Abstract

Telescopers for a function are linear differential (resp. difference) operators annihilating the definite integral (resp. definite sum) of this function. They play a key role in Wilf–Zeilberger theory and algorithms for computing them have been extensively studied in the past 30 years. In this paper, we introduce the notion of telescopers for differential forms with D-finite function coefficients. These telescopers appear in several areas of mathematics, for instance parametrized differential Galois theory and mirror symmetry. We give a sufficient and necessary condition for the existence of telescopers for a differential form and describe a method to compute them if they exist. Algorithms for verifying this condition are also given.

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Authors and Affiliations

  1. KLMM, AMSS, Chinese Academy of Sciences and School of Mathematics, University of Chinese Academy of Sciences, Beijing, 100190, China

    Shaoshi Chen, Ruyong Feng & Ziming Li

  2. Department of Mathematics, North Carolina State University, Raleigh, 27695-8205, USA

    Michael F. Singer

  3. Cheriton School of Computer Science, University of Waterloo, Ontario, N2L 3G1, Canada

    Stephen M. Watt

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  1. Shaoshi Chen
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  3. Ziming Li
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Correspondence to Ruyong Feng.

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S. Chen and Z. Li were partially supported by the National Key R &D Program of China (No. 2023YFA1009401), the NSFC Grants (Nos. 12271511 and 11688101), CAS Project for Young Scientists in Basic Research (Grant No. YSBR-034), and the CAS Fund of the Youth Innovation Promotion Association (No. Y2022001). R. Feng was partially supported by the NSFC Grants 11771433, Beijing Natural Science Foundation under Grant Z190004 and the National Key Research and Development Project 2020YFA0712300, M.F. Singer was partially supported by a Grant from the Simons Foundation (#349357, Michael Singer). S.M. Watt was partially supported by a Discovery Grant from the Canadian Natural Sciences and Engineering Research Council.

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Chen, S., Feng, R., Li, Z. et al. Telescopers for differential forms with one parameter. Sel. Math. New Ser. 30, 36 (2024). https://doi.org/10.1007/s00029-024-00926-6

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