A counterexample to the “hot spots" conjecture.
Burdzy, Krzysztof, Werner, Wendelin (1999)
Annals of Mathematics. Second Series
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Burdzy, Krzysztof, Werner, Wendelin (1999)
Annals of Mathematics. Second Series
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J. Mennicke, J. Elstrodt, F. Grunewald (1990)
Inventiones mathematicae
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H. Iwaniec (1985)
Banach Center Publications
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Valentin Blomer, Djordje Milićević (2015)
Journal of the European Mathematical Society
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We prove upper bounds for sums of Kloosterman sums against general arithmetic weight functions. In particular, we obtain power cancellation in sums of Kloosterman sums over arithmetic progressions, which is of square-root strength in any fixed primitive congruence class up to bounds towards the Ramanujan conjecture.
Henryk Iwaniec (1990)
Acta Arithmetica
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F. Beukers (1981)
Acta Arithmetica
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András Biró (2003)
Acta Arithmetica
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C. Greither, Radan Kučera (2008)
Acta Arithmetica
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G. Grekos, L. Haddad, C. Helou, J. Pihko (2005)
Acta Arithmetica
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Paule, Peter (1996)
Experimental Mathematics
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András Biró (2003)
Acta Arithmetica
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G. Besson (2009)
Bollettino dell'Unione Matematica Italiana
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W. Narkiewicz (1977)
Colloquium Mathematicae
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K. Kubota (1977)
Acta Arithmetica
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Qassem M. Al-Hassan, Mowaffaq Hajja (2015)
Applicationes Mathematicae
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In investigating a certain optimization problem in biogeography, Simon [IEEE Trans. Evolutionary Comput. 12 (2008), 702-713] encountered a certain specially structured tridiagonal matrix and made a conjecture regarding its eigenvalues. A few years later, the validity of the conjecture was established by Igelnik and Simon [Appl. Math. Comput. 218 (2011), 195-201]. In this paper, we give another proof of this conjecture that is much shorter, almost computation-free, and does not resort...
Fuzhen Zhang (2016)
Special Matrices
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We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top conjecture†, Lieb permanent dominance conjecture, Bapat and Sunder conjecture† on Hadamard product and diagonal entries, Chollet conjecture on Hadamard product, Marcus conjecture on permanent of permanents, and several other conjectures. Some of these conjectures are recently settled; some are still open.We...