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作者单位:Geoffrey D. Smith (1) <br> Lynnelle Ye (2) <br><br>1. Department of Mathematics, Yale University, 10 Hillhouse Avenue, New Haven, CT, 06511, USA <br> 2. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA <br>
刊物类别:Mathematics and Statistics
刊物主题:Mathematics<br>Number Theory<br>Field Theory and Polynomials<br>Combinatorics<br>Fourier Analysis<br>Functions of a Complex Variable<br>
出版者:Springer U.S.
ISSN:1572-9303
文摘
Let \(p(n)\) be the partition function. Ahlgren and Ono conjectured that every arithmetic progression contains infinitely many integers \(N\) for which \(p(N)\) is not congruent to \(0\;(\mathrm{mod}\;3)\). Radu proved this conjecture in 2010 using the work of Deligne and Rapoport. In this note, we give a simpler proof of Ahlgren and Ono’s conjecture in the special case where the modulus of the arithmetic progression is a power of \(3\) by applying a method of Boylan and Ono and using the work of Bellaïche and Khare generalizing Nicolas and Serre’s results on the local nilpotency of the Hecke algebra.