Integrals Involving Rudin-Shapiro Polynomials and Sketch of a Proof of\n Saffari's Conjecture

2016/05/21 by Shalosh B. Ekhad, Doron Zeilberger, Ekhad, Shalosh B. +1
Mathematics · #Advanced Combinatorial Mathematics #Analytic Number Theory Research #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.1605.06679

Abstract

Continuing pioneering work of Christophe Doche and Laurent Habsieger from\n2004, we develop computer algebra algorithms, implemented in Maple, for finding\nthe (necessarily rational) generating function for any integral of products,\nand in particular, moments, of Rudin-Shapiro polynomials. We generate a lot of\noutput, and confirm again a conjecture of Saffari for the asymptotics for small\n(and not so small) powers. We also confirm, for small powers, a related, more\ngeneral, conjecture, of Hugh Montgomery. Finally, we outline a proof of\nSaffari's full conjecture, that we believe can be turned into a full proof. [In\nthis version we report that Brad Rodgers has independently found a (complete!)\nproof of Saffari's conjecture here http://arxiv.org/abs/1606.01637] .\n

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