Results 21 to 30 of about 70 (62)
Contributions to the fixed point theory of diagonal operators [PDF]
Fixed Point Theory and Applications, 2016 AbstractIn this paper, we introduce the notion of diagonal operator, we present the historical roots of diagonal operators and we give some fixed point theorems for this class of operators. Our approaches are based on the weakly Picard operator technique, difference equation techniques, and some fixed point theorems for multi-valued operators.
Petruşel, Adrian +2 more
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Density of rational points on diagonal quartic surfaces [PDF]
Algebra & Number Theory, 2010 Let a,b,c,d be nonzero rational numbers whose product is a square, and let V be the diagonal quartic surface in PP^3 defined by ax^4+by^4+cz^4+dw^4=0. We prove that if V contains a rational point that does not lie on any of the 48 lines on V or on any of the coordinate planes, then the set of rational points on V is dense in both the Zariski topology ...
Logan, Adam +2 more
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Diagonalization, uniformity, and fixed-point theorems
Information and Computation, 1992 New fixed-point theorems for subrecursive classes are derived, together with a widely applicable theorem on the uniformity of certain reductions. The present formulation extends the main theorem of \textit{U. Schöning} ``A uniform approach to obtain diagonal sets for complexity classes'' [Theor. Comput. Sci.
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Cyclotomic Points and Algebraic Properties of Polygon Diagonals
, 2019 14 pages, 2 tables, 1 figure. Sage code included in ancillary file. Comments welcome!
Grubb, Thomas, Wolird, Christian
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Rational points on linear slices of diagonal hypersurfaces [PDF]
Nagoya Mathematical Journal, 2015 Abstract An asymptotic formula is obtained for the number of rational points of bounded height on the class of varieties described in the title line. The formula is proved via the Hardy-Littlewood method, and along the way we establish two new results on Weyl sums that are of some independent interest.
Brüdern, Jörg, Robert, Olivier
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Rational Points on Diagonal Cubic Surfaces
, 2014 We show under the assumption that the Tate-Shafarevich group of any elliptic curve over the rational numbers is finite that the cubic surface $x_1^3 + p_1p_2x_2^3 + p_2p_3x_3^3 + p_3p_1x_4^3 = 0$ has a rational point, where $p_1, p_2$ and $p_3$ are rational primes congruent to $2$ or $5$ modulo $9$.
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Rational points on diagonal quartic surfaces
, 2010 5 ...
Elsenhans, Andreas-Stephan
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Heegner points, Stark-Heegner points and diagonal classes
, 2020 Peer ...
Bertolini, Massimo +4 more
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Deflation for the Off-Diagonal Block in Symmetric Saddle Point Systems
SIAM Journal on Matrix Analysis and Applications28 pages, 13 ...
Andrei Dumitrasc +2 more
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The Asymptotics of Points of Bounded Height on Diagonal Cubic and Quartic Threefolds
, 2006 For the families ax3 = by3 + z3 + v3 + w3, a, b = 1, ... ,100, and ax4 = by4 + z4 + v4 + w4, a, b = 1, ... ,100, of projective algebraic threefolds, we test numerically the conjecture of Manin (in the refined form due to Peyre) about the asymptotics of points of bounded height on Fano varieties.
Elsenhans, Andreas-Stephan +2 more
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