Papers available in the arXiv



  • [LINK] P. Candela, F. Chamizo, and A. Córdoba. On sets with missing differences in compact abelian groups. arXiv:2408.09301 [math.CO], 2024.
  • [LINK] F. Chamizo and F. de la Hoz. Regular polygonal vortex filament evolution and exponential sums. arXiv:2403.17758 [math.NT], 2024.
  • [LINK] F. Chamizo, D. Raboso, and O. P. Santillán. Plateaux of probability for the expanded quantum infinite well. arXiv:2409.06058 [quant-ph], 2024.
  • [LINK] F. Chamizo. Correlation and lower bounds of arithmetic expressions. arXiv:2305.07277 [math.NT], 2023.
  • [LINK] F. Chamizo and O. Santillán. About the quantum Talbot effect on the sphere. arXiv:2302.11063 [quant-ph], 2023.
  • [LINK] F. Chamizo and O. Santillán. Exact quantum revivals for the Dirac equation. arXiv:2309.12471 [quant-ph], 2023.
  • [LINK] F. Chamizo and J. Jiménez-Urroz. Extendable orthogonal sets of integral vectors. arXiv:2203.10635 [math.NT], 2022.
  • [LINK] F. Chamizo and O. Santillán. Current induction and macroscopic forces for superconducting strings. arXiv:2212.09827 [hep-th], 2022.
  • [LINK] F. Chamizo. A simple evaluation of a theta value and the Kronecker limit formula. arXiv:2107.07245 [math.NT], 2021.
  • [LINK] A. Bostan, F. Chamizo, and M. P. Sundqvist. On an integral identity. arXiv:2002.10682 [math.CA], 2020.
  • [LINK] F. Chamizo. The additive problem for the number of representations as a sum of two squares. arXiv:2009.01667 [math.NT], 2020.
  • [LINK] F. Chamizo and J. Jiménez-Urroz. Primes represented by quadratic polynomials via exceptional characters. arXiv:2011.05398 [math.NT], 2020.
  • [LINK] D. Alonso-Orán, F. Chamizo, Á. D. Martínez, and A. Mas. Pointwise monotonicity of heat kernels. arXiv:1807.11072v1 [math.CA], 2018.
  • [LINK] F. Chamizo, A. Córdoba, and A. Ubis. Fourier series in BMO with number theoretical implications. arXiv:1812.08747 [math.CA], 2018.
  • [LINK] F. Chamizo, E. Gallardo-Gutiérrez, M. Monsalve-López, and A. Ubis. Invariant subspaces for Bishop operators and beyond. arXiv:1812.08059 [math.FA], 2018.
  • [LINK] F. Chamizo and R. J. Miatello. Sums of squares in real quadratic fields and hilbert modular groups. arXiv:1812.10725 [math.NT], 2018.
  • [LINK] F. Chamizo and J. Granados. A short proof of sharp Weyl's law for the special orthogonal group. arXiv:1706.05160 [math.AP], 2017.
  • [LINK] F. Chamizo and C. Pastor. Lattice points in bodies of revolution II. arXiv:1709.08593 [math.NT], 2017.
  • [LINK] F. Chamizo and A. Gonzalez-Arroyo. Tachyonic instabilities in 2+1 dimensional Yang-Mills theory and its connection to number theory. arXiv:1610.07972 [hep-th], 2016.
  • [LINK] F. Chamizo and C. Pastor. Lattice points in elliptic paraboloids. arXiv:1611.04498 [math.NT], 2016.
  • [LINK] F. Chamizo, I. Petrykiewicz, and S. Ruiz-Cabello. The Hölder exponent of some Fourier series. arXiv:1504.04998 [math.CA], 2015.
  • [LINK] F. Chamizo and D. Raboso. Lattice points in the 3-dimensional torus. arXiv:1412.5956 [math.NT], 2014.
  • [LINK] F. Chamizo and A. Ubis. Multifractal behavior of polynomial Fourier series. arXiv:1208.6533 [math.NT], 2012.
  • [LINK] F. Chamizo. Non-Euclidean visibility problems. arXiv:math/0607699 [math.NT], 2006.

Last ten publications
  • [LINK] F. Chamizo. Correlation and lower bounds of arithmetic expressions. Acta Arith., 214:257-269, 2024.
  • [LINK] F. Chamizo and F. de la Hoz. Regular Polygonal Vortex Filament Evolution and Exponential Sums. Acta Appl. Math., 194:Paper No. 8, 2024.
  • [LINK] F. Chamizo and D. Raboso. Digits, Primes and, of course, Pi. Amer. Math. Monthly, 131(8):718-721, 2024.
  • [LINK] F. Chamizo and O. P. Santillán. Exact quantum revivals for the Dirac equation. Phys. Rev. A, 109(2):Paper No. 022231, 2024.
  • [LINK] F. Chamizo and A. Ubis. Ampère's Law and Vector Calculus. Math. Mag., 97(4):406-408, 2024.
  • [LINK] D. Alonso-Orán, F. Chamizo, Ángel D. Martínez, and Albert Mas. Pointwise monotonicity of heat kernels. Rev. Mat. Complut., 36(1):207-220, 2023.
  • F. Chamizo. A simple linear algebra approach to {Pauli} spinors. Eur. J. Phys., 44(1):7, 2023. Id/No 015401.
  • [LINK] F. Chamizo and B. Martin. The approximate functional equation of some Diophantine series. Monatsh. Math., 202(1):41-52, 2023.
  • [LINK] F. Chamizo and O. P. Santillán. About the quantum Talbot effect on the sphere. J. Phys. A, 56(25):Paper No. 255302, 20, 2023.
  • [LINK] F. Chamizo and O. P. Santillán. Current induction and macroscopic forces for superconducting strings. Phys. Rev. D, 107(7):Paper No. 075015, 21, 2023.

Other publications
  • [LINK] A. Pérez, M. Prieto-Alaiz, F. Chamizo, E. Liebscher, and M. Úbeda Flores. Nonparametric estimation of the multivariate Spearman's footrule: A further discussion. Fuzzy Sets and Systems, 467:108489, 2023.
  • [LINK] F. Chamizo. The additive problem for the number of representations as a sum of two squares. Mediterr. J. Math., 19(1):Paper No. 44, 17, 2022.
  • [LINK] F. Chamizo. La identidad de Amitsur-Levitzki. Gac. R. Soc. Mat. Esp., 25(1):148, 2022.
  • [LINK] F. Chamizo. A simple evaluation of a theta value, the Kronecker limit formula and a formula of Ramanujan. Ramanujan J., 59(3):947-954, 2022.
  • [LINK] F. Chamizo and J. Jiménez-Urroz. Extendable orthogonal sets of integral vectors. Res. Math. Sci., 9(4):Paper No. 59, 13, 2022.
  • [LINK] A. Bostan, F. Chamizo, and M. P. Sundqvist. On an Integral Identity. Amer. Math. Monthly, 128(8):737-743, 2021.
  • [LINK] F. Chamizo. Un resultado de Kubilyus y Linnik. Gac. R. Soc. Mat. Esp., 24(1):146, 2021.
  • [LINK] F. Chamizo, J. Fernández-Sánchez, and M. Úbeda Flores. Construction of copulas with hairpin support. Mediterr. J. Math., 18(4):Paper No. 155, 19, 2021.
  • [LINK] F. Chamizo and J. Jiménez Urroz. Primes represented by quadratic polynomials via exceptional characters. Arch. Math. (Basel), 117(2):147-154, 2021.
  • [LINK] F. Chamizo and B. Martin. The convergence of certain Diophantine series. J. Number Theory, 229:179-198, 2021.
  • [LINK] F. Chamizo. Sumando de la W a la Z. Gac. R. Soc. Mat. Esp., 23(1):163-175, 2020.
  • [LINK] F. Chamizo, A. Córdoba, and A. Ubis. Fourier series in BMO with number theoretical implications. Math. Ann., 376(1-2):457-473, 2020.
  • [LINK] F. Chamizo, E. A. Gallardo-Gutiérrez, M. Monsalve-López, and A. Ubis. Invariant subspaces for Bishop operators and beyond. Adv. Math., 375:107365, 25, 2020.
  • [LINK] F. Chamizo and Jos\'{e} Granados. A short proof of a sharp Weyl law for the special orthogonal group. J. Spectr. Theory, 10(1):311-322, 2020.
  • [LINK] F. Chamizo and R. J. Miatello. Sums of squares in real quadratic fields and Hilbert modular groups. Bull. Lond. Math. Soc., 52(1):244-259, 2020.
  • [LINK] F. Chamizo and C. Pastor. Lattice points in bodies of revolution II. Math. Nachr., 293(6):1074-1083, 2020.
  • [LINK] F. Chamizo. Morphisms and period matrices. Linear Algebra Appl., 582:103-113, 2019.
  • [LINK] F. Chamizo and C. Pastor. Lattice points in elliptic paraboloids. Publ. Mat., 63(1):343-360, 2019.
  • [LINK] F. Chamizo and A. González-Arroyo. Tachyonic instabilities in 2+1 dimensional Yang-Mills theory and its connection to number theory. J. Phys. A, 50(26):265401, 17, 2017.
  • [LINK] F. Chamizo, I. Petrykiewicz, and S. Ruiz-Cabello. The Hölder exponent of some Fourier series. J. Fourier Anal. Appl., 23(4):758-777, 2017.
  • [LINK] F. Chamizo. Un teorema de Javier Cilleruelo. Gac. R. Soc. Mat. Esp., 19(3):607-614, 2016.
  • [LINK] F. Chamizo and D. Raboso. Lattice points in the 3-dimensional torus. J. Math. Anal. Appl., 429(2):733-743, 2015.
  • [LINK] F. Chamizo and D. Raboso. On the Kuznetsov formula. J. Funct. Anal., 268(4):869-886, 2015.
  • [LINK] F. Chamizo and D. Raboso. Van der Corput method and optical illusions. Indag. Math. (N.S.), 26(5):723-735, 2015.
  • [LINK] F. Chamizo and D. Raboso. Distributional properties of powers of matrices. Czechoslovak Math. J., 64(139)(3):801-817, 2014.
  • [LINK] F. Chamizo and A. Ubis. Multifractal behavior of polynomial Fourier series. Adv. Math., 250:1-34, 2014.
  • [LINK] F. Chamizo and J. Jiménez-Urroz. Irreducibility and the distribution of some exponential sums. Finite Fields Appl., 23:53-59, 2013.
  • [LINK] F. Chamizo, D. Raboso, and S. Ruiz-Cabello. Exotic approximate identities and Maass forms. Acta Arith., 159(1):27-46, 2013.
  • [LINK] F. Chamizo and E. Cristóbal. The sphere problem and the L-functions. Acta Math. Hungar., 135(1-2):97-115, 2012.
  • [LINK] F. Chamizo. Hyperbolic lattice point problems. Proc. Amer. Math. Soc., 139(2):451-459, 2011.
  • [LINK] F. Chamizo. On twisted character sums. Arch. Math. (Basel), 96(5):417-421, 2011.
  • [LINK] F. Chamizo and Y. Fuertes. The number of mappings between compact Riemann surfaces. Osaka J. Math., 48(3):743-748, 2011.
  • [LINK] F. Chamizo, O. Gil, and D. Raboso. A propósito de la soledad de los números primos. Matematicalia, 7(2), 2011.
  • [LINK] F. Chamizo and D. Raboso. Fracciones bonitas. G.I.E. Pensamiento Matemático, 1:97-115, Oct 2011.
  • [LINK] F. Chamizo, D. Raboso, and S. Ruiz-Cabello. On Rowland's sequence. Electron. J. Combin., 18(2):Paper 10, 10, 2011.
  • [LINK] F. Chamizo and D. Raboso. Modular forms and almost integers (Spanish). Gac. R. Soc. Mat. Esp., 13(3):539-555, 2010.
  • [LINK] F. Chamizo, E. Cristóbal, and A. Ubis. Lattice points in rational ellipsoids. J. Math. Anal. Appl., 350(1):283-289, 2009.
  • [LINK] F. Chamizo. Atle Selberg: 1917-2007 (Spanish). Gac. R. Soc. Mat. Esp., 11(1):193-208, 2008.
  • [LINK] F. Chamizo. Lattice point counting and harmonic analysis. In Proceedings of the ``Segundas Jornadas de Teoría de Números'', Bibl. Rev. Mat. Iberoamericana, pages 83-99. Rev. Mat. Iberoamericana, Madrid, 2008.
  • [LINK] F. Chamizo. Euler and number theory. Gac. R. Soc. Mat. Esp., 10(2):407-426, 2007.
  • [LINK] F. Chamizo, E. Cristóbal, and A. Ubis. Visible lattice points in the sphere. J. Number Theory, 126(2):200-211, 2007.
  • [LINK] F. Chamizo and A. Ubis. Some Fourier series with gaps. J. Anal. Math., 101:179-197, 2007.
  • [LINK] F. Chamizo. Non-Euclidean visibility problems. Proc. Indian Acad. Sci. Math. Sci., 116(2):147-160, 2006.
  • [LINK] F. Chamizo, E. Cristóbal, and A. Ubis. The circle method. Gac. R. Soc. Mat. Esp., 9(2):465-481, 2006.
  • [LINK] F. Chamizo and A. Ubis. An average formula for the class number. Acta Arith., 122(1):75-90, 2006.
  • [LINK] F. Chamizo. Automorphic forms and differentiability properties. Trans. Amer. Math. Soc., 356(5):1909-1935 (electronic), 2004.
  • [LINK] F. Chamizo and A. Córdoba. A path integral approach to lattice point problems. J. Math. Pures Appl. (9), 81(10):957-966, 2002.
  • [LINK] F. Chamizo and A. Córdoba. Lattice points. In Margarita mathematica, pages 59-76. Univ. La Rioja, Logroño, 2001.
  • [LINK] F. Chamizo. Correlated sums of r(n). J. Math. Soc. Japan, 51(1):237-252, 1999.
  • [LINK] F. Chamizo and A. Córdoba. Differentiability and dimension of some fractal Fourier series. Adv. Math., 142(2):335-354, 1999.
  • [LINK] F. Chamizo. The circle problem. Gac. R. Soc. Mat. Esp., 1(3):435-437, 1998.
  • [LINK] F. Chamizo. Lattice points in bodies of revolution. Acta Arith., 85(3):265-277, 1998.
  • [LINK] F. Chamizo and A. Córdoba. Riemann fractals: numbers and figures. Gac. R. Soc. Mat. Esp., 1(1):37-47, 1998.
  • [LINK] F. Chamizo and H. Iwaniec. On the Gauss mean-value formula for class number. Nagoya Math. J., 151:199-208, 1998.
  • [LINK] F. Chamizo and J. Pomykała. Distribution of zeros of twisted automorphic L-functions with large level. Math. Z., 229(4):575-588, 1998.
  • [LINK] F. Chamizo. Sums of squares in z[sqrt(k)]. J. Théor. Nombres Bordeaux, 9(1):25-39, 1997.
  • [LINK] F. Chamizo and A. Córdoba. One-dimensional crystals and quadratic residues. J. Number Theory, 65(1):101-104, 1997.
  • [LINK] F. Chamizo. The large sieve in Riemann surfaces. Acta Arith., 77(4):303-313, 1996.
  • [LINK] F. Chamizo. Some applications of large sieve in Riemann surfaces. Acta Arith., 77(4):315-337, 1996.
  • [LINK] F. Chamizo and H. Iwaniec. Estimates for L-functions associated with some elliptic curves. Rocky Mountain J. Math., 26(3):951-958, 1996. Symposium on Diophantine Problems (Boulder, CO, 1994).
  • [LINK] F. Chamizo and H. Iwaniec. On the sphere problem. Rev. Mat. Iberoamericana, 11(2):417-429, 1995.
  • [LINK] F. Chamizo and A. Córdoba. The fractal dimension of a family of Riemann's graphs. C. R. Acad. Sci. Paris Sér. I Math., 317 (Erratum 320 https://shorturl.at/eiK59)(5):455-460, 1993.
  • L. Contreras Caballero and F. Chamizo. Criteria for distinguishing the character of degenerate quadratic forms. In Proceedings of the XVth Portuguese-Spanish Conference on Mathematics, Vol. I (Évora, 1990), pages 77-82, Évora, 1991. Univ. Évora.

Scope of research

Most of my production is ascribed to number theory but I have also touched other topics (mostly exploiting their relation to number theory). The following pie chart shows the proportion of the 63 first-level areas in MSC2020 (Wikipedia) covered by the primary and secondary classification of my papers.
pie_chart
The source is MathScinet and, when not available, zbMATH.

Summary of papers per topic: (53) Number theory; (7) Real functions; (7) Measure and integration; (6) Harmonic analysis on Euclidean spaces; (5) Quantum theory; (5) Linear and multilinear algebra; matrix theory; (4) Functions of a complex variable; (3) Special functions; (3) Partial differential equations; (3) History and biography; (3) Global analysis, analysis on manifolds; (2) Statistics; (2) Sequences, series, summability; (2) Probability theory and stochastic processes; (2) Convex and discrete geometry; (1) Topological groups, Lie groups; (1) Statistical mechanics, structure of matter; (1) Optics, electromagnetic theory; (1) Operator theory; (1) Mechanics of particles and systems; (1) Difference and functional equations; (1) Combinatorics; (1) Approximations and expansions; (1) Algebraic geometry; (1) Abstract harmonic analysis.
Click here for a linked list with references.

Brief Vitae


More detailed information can be found in the UAM Scientific portal.

ORCID: 0000-0003-2793-7920


Address

Departamento de Matemáticas and ICMAT
Facultad de Ciencias
Universidad Autónoma de Madrid
28049 Madrid. Spain

Education

  • Ph.D. in Mathematics. Universidad Autónoma de Madrid, 1994.
  • Expert in University teaching (UAM specific degree). Universidad Autónoma de Madrid, 2014.
  • Master in Theoretical Physics. Universidad Autónoma de Madrid, 2016.
Current position

Professor in Mathematics Department of Universidad Autónoma de Madrid (since 1997).

Research interests
 
Analytic Number Theory: spectral theory of automorphic forms, exponential and character sums, lattice point problems, applications to Harmonic Analysis. Algebraic Number Theory. Mathematical Physics.

Teaching experience
 
I have taught at Universidad Autónoma de Madrid a wide range of courses, covering Differential Geometry, Discrete Mathematics, Galois Theory, General Relativity, Group Theory, Linear Algebra, Mathematical Modelling, Number Theory, Numerical Analysis, Calculus, ODEs and Topology.
I have written numerous lecture notes for teaching purposes.

PhD supervision

  • Adrián Ubis. Questions of Arithmetic and Harmonic Analysis. Defended 1st September 2006
  • Elena Cristóbal. Three-dimensional lattice point problems. Defended 25th May 2009.
  • Dulcinea Raboso. Spectral, combinatoric and analytic methods in some problems in Number Theory. Defended 8th July 2014.
  • Serafín Ruiz-Cabello. Prime generators, approximate identities and multifractal functions. Defended 23rd May 2014.
  • Carlos Pastor. Modular forms and lattice counting problems. Defended 14th December 2018.
  • José Granados. Classic number theory in three different contexts. Defended 17th July 2020.

Selected talks

  • "Where is my spiral?''. 12th December 2019. Experimental Math Seminar. Rutgers University.
  • "Bishop operators and Diophantine approximation'''. 3rd December 2019. Université Paris-Est Créteil.
  • "Fourier series with gaps and arithmetic''. 21st March 2019. Université Paris-Est Créteil. Paris.
  • "Fractal and multifractal Fourier series''. 15th May 2014. The Hauteurs, Modularité et Transcendence. Marseille.
  • "Antonio Córdoba and Number Theory''. 26th June 2009. The Poetry of Analysis. Colegio Mayor Juan Luis Vives. Madrid.
  • "Lattice point problems''. 19th July 2007. Plenary talk. Segundas jornadas de teoría de números. Colegio mayor Juan Luis Vives. Madrid.
  • "Some applications of the large sieve''. 21st June 2003. Invited talk. Joint Meeting RSME-AMS. Seville.
  • "Modular forms, fractals and differentiability''. 19th September 2001. Invited talk. Mathematisches Forschungsinstitut Oberwolfach.
  • "Lattice points under random graphs''. 7th September 2000. Invited talk. C.I.R.M. Luminy-Marsella.
  • "The hyperbolic circle problem and its applications''. 14th April 2000. Invited talk. Workshop on Recent Trends in Number Theory. Institute for Advanced Study. Princeton.
  • "Trigonometric sums and Number Theory''. 29th January 2000. Plenary talk. Primer Congreso de la Real Sociedad Matemática Española.Universidad de Alcalá de Henares.

Committee and managing activities

  • Member of the editorial board of Revista Matemática Iberoamericana since 2001.
  • Member of the organizing committee of the Polish-Spanish joint meeting, Lodz (2021).
  • Member of the editorial board of the electronic journal Pensamiento Matemático (Mathematical Thinking) since 2012.
  • Member of the scientific committee of the Quintas Jornadas de Teoría de Números held in Seville (Spain) in July 2013.
  • Member of the scientific committee of the Cuartas Jornadas de Teoría de Números  held in Bilbao (Spain) in July 2011.
  • Member of the program committee of the Conference in honour of Antonio Córdoba on the occasion of his 60th birthday (2009).
  • Coordinator in the 49th International Mathematical Olympiad Madrid 2008.
  • Editor (joint with Adolfo Quirós) of the special issue of Mathematical Intelligencer on the occasion of the ICM2006.
  • Member of the Teaching Committee in Mathematics Department at UAM during the courses 2003-2004 and 2004-2005.
  • Departamental coordinator (in UAM) of the Socrates-Erasmus program from 2001 to 2005.

  1. MITx 8.05x: Mastering Quantum Mechanics. (certificate)
  2. CS184.1x: Foundations of Computer Graphics. (certificate)
  3. MITx 8.06x: Applications of Quantum Mechanics. (certificate)
  4. MITx 3.032.1x: Mechanical Behavior of Materials: Linear Elastic Behavior. (certificate)
  5. MITx 2.25.1x: Advanced Fluid Mechanics 1: Fundamentals. (certificate)
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