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A NNALES DE L INSTITUT F OURIERVOLKER D NGER padic interpolation of convolutions of Hilbert modular forms Annales de linstitut Fourier, tome 47, no 2 (1997), p. 365428 http://www.numdam.org/item?idAIF_1997__47_2_365_0
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To fill out p-adic interpolation of convolutions, follow these steps:
02
Begin by computing the convolution of the given p-adic sequences.
03
Use the Chinese Remainder Theorem to lift this convolution to the integers.
04
Perform p-adic interpolation by evaluating the lifted convolution at p-adic integers.
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Finally, reconstruct the p-adic interpolant by using the inverse Chinese Remainder Theorem.

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Mathematicians and researchers working in number theory and algebraic geometry may require p-adic interpolation of convolutions.
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It is also useful in cryptography, signal processing, and other areas where computations involve p-adic numbers.
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p-adic interpolation of convolutions is a mathematical technique used in number theory that allows the study of sequences of numbers and functions through the lens of p-adic numbers, providing insights into their properties and relationships via convolution operations.
Mathematicians, researchers, and professionals in the field of number theory and algebraic geometry who are engaged in projects requiring p-adic analysis and convolution techniques may need to 'file' their work with appropriate academic or research bodies.
Filling out p-adic interpolation of convolutions typically involves defining the specific sequences, the desired properties, and formulating the convolution sums or integrals according to the rules of p-adic mathematics.
The purpose of p-adic interpolation of convolutions is to analyze and deduce properties of sequences or functions within the framework of p-adic numbers, allowing for a systematic study of their convergence and divergence principles.
Required information typically includes the sequences being analyzed, the parameters of convolution operations, the context in which p-adic interpolation is applied, and any applicable results or findings.
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