Mizan R. Khan

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All published works

Action	Title	Year	Authors
+	Interior Hulls of Clean Lattice Parallelograms and Continued Fractions	2024	Gabriel Khan Mizan R. Khan Riaz R. Khan Peng Zhao
+	Counting Clean Triangles	2022	Mizan R. Khan Riaz R. Khan
+ PDF Chat	A Conjectural Inequality for Visible Points in Lattice Parallelograms	2021	Gabriel Khan Mizan R. Khan Joydip Saha Peng Zhao
+	To count clean triangles we count on $imph(n)$	2020	Mizan R. Khan Riaz R. Khan
+	A Conjectural Inequality for Visible Points in Lattice Parallelograms	2019	Gabriel Khan Mizan R. Khan Joydip Saha Peng Zhao
+	White’s Theorem	2017	Mizan R. Khan Karen Rogers
+	An Exposition of White's Characterization of Empty Lattice Tetrahedra	2016	Mizan R. Khan Karen Rogers
+	Two Combinatorial Geometric Problems Involving Modular Hyperbolas	2013	Mizan R. Khan Richard Magner Steven Senger Arne Winterhof
+	Two Combinatorial Geometric Problems Involving Modular Hyperbolas	2013	Mizan R. Khan Richard Magner Steven Senger Arne Winterhof
+	Karatsuba Solitaire	2011	Therese A. Hart Gabriel Khan Mizan R. Khan
+	Modular Hyperbolas and the Coefficients of (x –1 + 6 + x) k	2011	Mizan R. Khan
+ PDF Chat	The cardinality of the value sets modulo<i>n</i>of<i>x</i><sup>2</sup>+<i>x</i><sup>−2</sup>and<i>x</i><sup>2</sup>+<i>y</i><sup>2</sup>	2010	Sara Hanrahan Mizan R. Khan
+	Geometric properties of points on modular hyperbolas	2010	Kevin Ford Mizan R. Khan Igor E. Shparlinski
+	The cardinality of the value sets modulo n of x 2 C x 2 and x 2 C y 2	2010	Sara Hanrahan Mizan R. Khan
+	Sums and Differences of the Coordinates of Points on Modular Hyperbolas	2009	Dennis Eichhorn Mizan R. Khan Alan H. Stein Christian L. Yankov
+ PDF Chat	On the Convex Closure of the Graph of Modular Inversions	2008	Mizan R. Khan Igor E. Shparlinski Christian L. Yankov
+	On the Convex Closure of the Graph of Modular Inversions	2007	Mizan R. Khan Igor E. Shparlinski Christian L. Yankov
+	On the maximal difference between an element and its inverse in residue rings	2005	Kevin Ford Mizan R. Khan Igor E. Shparlinski Christian L. Yankov
+ PDF Chat	On the maximal difference between an element and its inverse modulo n	2003	Mizan R. Khan Igor E. Shparlinski
+	None	2002	József Beck Mizan R. Khan
+	A Counting Formula for Primitive Tetrahedra in<i>Z</i><sup>3</sup>	1999	Mizan R. Khan
+	A Counting Formula for Primitive Tetrahedra in Z 3	1999	Mizan R. Khan
+	Computation of Partial Zeta Values ats=0 over a Totally Real Cubic Field	1996	Mizan R. Khan
+	Computation of partial zeta values at S = 0 for a totally real cubic base field	1990	Mizan R. Khan

Common Coauthors

Coauthor	Papers Together
Igor E. Shparlinski	5
Christian L. Yankov	4
Gabriel Khan	4
Riaz R. Khan	3
Peng Zhao	3
Richard Magner	2
Joydip Saha	2
Karen Rogers	2
Sara Hanrahan	2
Steven Senger	2
Arne Winterhof	2
Kevin Ford	1
Kevin Ford	1
Therese A. Hart	1
József Beck	1
Dennis Eichhorn	1
Alan H. Stein	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	On the Distribution of Inverses Modulon	1996	Wenpeng Zhang	5
+	The Distribution of Zeros of an Irreducible Curve over a Finite Field	1996	Zhiyong Zheng	5
+	None	2002	József Beck Mizan R. Khan	4
+	Distribution of Values of Rational Maps on the F p -Points on an Affine Curve	2002	Marian Vâjâitu Alexandru Zaharescu	4
+ PDF Chat	On the maximal difference between an element and its inverse modulo n	2003	Mizan R. Khan Igor E. Shparlinski	4
+	A Counting Formula for Primitive Tetrahedra in<i>Z</i><sup>3</sup>	1999	Mizan R. Khan	4
+	On the distribution of rational functions along a curve over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math> and residue races	2005	Andrew Granville Igor E. Shparlinski Alexandru Zaharescu	3
+	An Introduction to the Theory of Numbers. By G. H. Hardy and E. M. Wright. 2nd edition. Pp. xvi, 407 25s. 1945. (Oxford)	1946	T. A. A. B.	3
+ PDF Chat	On the distribution of the F<sub>p</sub>-points on an affine curve in r dimensions	2001	Cristian Cobeli Alexandru Zaharescu	3
+	Lattice point simplices	1986	Bruce Reznick	3
+ PDF Chat	Zero-Free Regions for Dirichlet L-Functions, and the Least Prime in an Arithmetic Progression	1992	D. R. Heath‐Brown	3
+	On Exponential Sums in Finite Fields	1966	Enrico Bombieri	3
+ PDF Chat	Introduction to Analytic Number Theory	1976	Tom M. Apostol	2
+ PDF Chat	On convex lattice polygons	1976	P. R. Scott	2
+	On the Difference Between An Integer and Its Inverse Modulo n	1995	W.P. Zhang	2
+	Zero-free regions for Dirichlet L-functions	1999	H. Li	2
+	Prime Numbers: A Computational Perspective	2012	Richard E. Crandall Carl Pomerance	2
+	On the Volume of Lattice Polyhedra	1957	J. E. Reeve	2
+	On Kloosterman's sum	1961	T. Estermann	2
+	The average order of an arithmetic function	1956	Emil Grosswald	2
+ PDF Chat	An introduction to the theory of numbers	1960	G. H. Hardy	2
+	On the maximal difference between an element and its inverse in residue rings	2005	Kevin Ford Mizan R. Khan Igor E. Shparlinski Christian L. Yankov	2
+ PDF Chat	The distribution of integers with a divisor in a given interval	2008	Kevin Ford	2
+	Entiers à diviseurs denses 1	1997	Éric Saïas	2
+	On the frequency of numbers containing prime factors of a certain relative magnitude	1930	Kern W. Dickman	2
+	Lectures on the Geometry of Numbers	1989	Carl Ludwig Siegel K. Chandrasekharan	2
+	Divisors	1988	Richard R. Hall Gérald Tenenbaum	1
+	Arithmetical Functions	1994	Wolfgang Schwarz Jürgen Spilker	1
+	On the number of distances between the coordinates of points on modular hyperbolas	2007	Igor E. Shparlinski Arne Winterhof	1
+ PDF Chat	A Lower Bound for the Volume of Strictly Convex Bodies with many Boundary Lattice Points	1963	George E. Andrews	1
+ PDF Chat	On the distribution of points on multidimensional modular hyperbolas	2007	Igor E. Shparlinski	1
+	Clean Lattice Tetrahedra	2006	Bruce Reznick	1
+	Mean Values of Quadratic Twists of AutomorphicL-functions	1996	Yuanli Zhang	1
+ PDF Chat	Primes in Arithmetic Progressions to Large Moduli. III	1989	E. Bombieri John Friedlander H. Iwaniec	1
+ PDF Chat	�ber die konvexe H�lle von n zuf�llig gew�hlten Punkten	1963	A. R�nyi Robert A. Sulanke	1
+	On Some Exponential Sums	1948	André Weil	1
+ PDF Chat	Primes in arithmetic progressions to large moduli	1986	Enrico Bombieri John Friedlander Henryk Iwaniec	1
+ PDF Chat	A lower bound for the volume of strictly convex bodies with many boundary lattice points	1963	George E. Andrews	1
+ PDF Chat	Pure and mixed exponential sums	1999	Todd Cochrane Zhiyong Zheng	1
+	The volume of a lattice polyhedron	1963	I. G. Macdonald	1
+	Introduction to Analytic Number Theory	1976	Tom M. Apostol	1
+ PDF Chat	On Bombieri's estimate for exponential sums	1971	J. H. H. Chalk Robert A. Smith	1
+	A proof of Coleman's conjecture	2006	Krzysztof Kołodziejczyk Daria Olszewska	1
+	A Classical Introduction to Modern Number Theory	1982	Kenneth Ireland Michael Rosen	1
+ PDF Chat	The cardinality of the value sets modulo<i>n</i>of<i>x</i><sup>2</sup>+<i>x</i><sup>−2</sup>and<i>x</i><sup>2</sup>+<i>y</i><sup>2</sup>	2010	Sara Hanrahan Mizan R. Khan	1
+	Introduction to Analytic and Probabilistic Number Theory	2015	Gérald Tenenbaum	1
+	Counting Squares in ℤ<sub>n</sub>	1996	Walter D. Stangl	1
+	Pick's Formula via the Weierstrass ℘-Function	1995	Ricardo Vázquez Díaz Sinai Robins	1
+	There are Infinitely Many Carmichael Numbers	1994	W. R. Alford Andrew Granville Carl Pomerance	1
+ PDF Chat	Lectures on the geometry of numbers	1990	K. Chandrasekharan	1