Preprints, Papers, Notes

These notes are in reverse chronological order of when they were written, not in the order in which they were published. Some of them are still unfinished and have never been submitted anywhere. For a list of published works click here

1. sh-126: A Linear--Logical Semantics of Graded Neural Networks, Valeria de Paiva, Tony Shaska

2. sh-120: Lie Algebras and Graded Neural Networks, L. Carbone, E. Jurisich, T. Shaska

3. sh-113: Faltings heights and Weighted heights, Andrew Obus, Tony Shaska

4. sh-112: Stacky Heights and Zeta Functions of Weighted Hypersurfaces, S. Salami, T. Shaska

5. sh-111: Internalizing Tools as Morphisms in Graded Transformers

6. sh-107: Graded Quantum Codes,
   Master Thesis, Computer Science and Engineering, Oakland University (2026)

7. sh-102: Graded Quantum Codes: From Weighted Algebraic Geometry to Homological Chain Complexes

8. sh-99: Categorical Hypergraph Models for Distributed Data Fabrics
   Decision-Making, Optimization, and Data Analysis: Theory and Applications.
   Springer Optimization and Its Applications

9. sh-98: Hitchin spinors and genus 2 curves, A. Clingher, A. Malmendier, T. Shaska

10. sh-97: Finsler Metric Clustering in Weighted Projective Spaces
    Advances in Pure and Applied Mathematics (submitted)

11. sh-95: Graded Transformers: A Symbolic-Geometric Approach to Structured Learning

12. sh-94: Arithmetic Sparsity and Cohomological Obstructions in WPS, (Int. Journal Number Theory)

13. sh-93: Isogenies, Kummer surfaces, and theta functions
    NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur.  Vol. 66, pg. 1-55. DOI: 10.3233/NICSP250002

14. sh-91: Rational Points and Zeta Functions of Humbert Surfaces over F_q
    NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur.  Vol. 66, pg. 92-122;  DOI: 10.3233/NICSP250004

15. sh-90: Weighted Heights and GIT Heights.  Jour. Algeb. Comb., 2026

16. sh-89:  Graded Neural Networks, Int, J. Data Sci. Math. Sci., 2025  

17. sh-87: Rational points of weighted hypersurfaces over finite fields, FFA (submitted)

18. sh-86: Neuro-Symbolic Learning for Irreducible Sextics: Unveiling Probabilistic Trends in Polynomials 

19. sh-85: Galois Groups of Quintics: A Neurosymbolic Approach to Polynomial Classification 

20. 2024-06: A Neurosymbolic Framework for Geometric Reduction of Binary Forms ,Cont. Math.  Vol. 835,  2026, pg. 173-194

21. 2024-05: Polynomials, Galois groups,  and Database-Driven Arithmetic, Cont. Math. Volume 835,  2026, pg. 231-305

22. 2024-04: Rational Functions on the Projective Line from a Computational Viewpoint 

23. 2024-03: Machine learning for M_2 and an application to isogeny based cryptography  Jour. Alg. Comb,  61, 23 (2025).

24. 2024-02: Artificial neural networks on graded vector spaces   Cont. Math,  Vol. 835, 2026, pg. 1-72

25. 2024-01: Equations for generalized superelliptic Riemann surfaces

26. 2023-01:   Vojta's conjecture on weighted projective varieties, Europ. Jour. Math.,  11, 12 (2025).  

27. 2022-1: Local and global heights on weighted projective varieties, Houston J. Math. Vol. 49, #3, (2023), pg. 603-636

28. 2021-2: Arithmetic inflection of superelliptic curves, Michigan Math. J.  75 (2025), no. 4, 675–724.

29. 2021-1: Geometry of Prym varieties for certain bielliptic curves of genus three and five,
    Pure Appl. Math. Q.  17  1739--1784  (2021)  https://doi.org/10.4310/PAMQ.2021.v17.n5.a5 

30. 2020-1: Reduction of superelliptic Riemann surfaces, Contemporary Math. 776  227--247  (2022)   

31. 2020-i: Integrable systems: a celebration of Emma Previato's 65th birthday, Donagi/Shaska, 458,1--12  (2020) 

32. 2020-ii: Algebraic geometry: a celebration of Emma Previato's 65th birthday, Donagi/Shaska,  1--12  (2020)

33. 2019-5: The addition on Jacobian varieties from a geometric viewpoint

34. 2019-4: From hyperelliptic to superelliptic curves, Albanian J. Math.  13  107--200  (2019)

35. 2019-3:  Superelliptic curves with many automorphisms and CM Jacobians, Math. Comp.  90  2951--2975  (2021)
    https://doi.org/10.1090/mcom/3639 

36. 2019-2: On isogenies among certain abelian surfaces,  Michigan Math. J.  71  (2022),  227--269.
       https://doi.org/10.1307/mmj/20195790 

37. 2019-1:  Weighted greatest common divisors and weighted heights,
    J. Number Theory  213  319--346  (2020)  https://doi.org/10.1016/j.jnt.2019.12.012  

38. 2018-6: On automorphisms of algebraic curves,
    Contemporary Math. 724  175--212  (2019) https://doi.org/10.1090/conm/724/14590 

39. 2018-5: Kay Magaard (1962--2018), Albanian J. Math.  12  33--35  (2018) https://albanian-j-math.com/archives/2018-05.pdf

40. 2018-4: Computing heights on weighted projective spaces,
    Contemporary Math.  724  149--160  (2019) https://doi.org/10.1090/conm/724/14588   

41. 2018-3:  Six line configurations and string dualities, A.Clingher, A.Malmendier, T. Shaska, 
    Comm. Math. Phys.  371  159--196  (2019) https://doi.org/10.1007/s00220-019-03372-0 

42. 2018-2: On the discriminant of certain quadrinomials,  Contemporary Math. 724  55--72  (2019)   

43. 2018-1: Curves, Jacobians, and cryptography, Contemporary Math. 724  279--344  (2019)   

44. 2017-4: Coing Theory, Alfred J. Menezes, Paul C. van Oorschot, D. Joyner, T. Shaska, D. R. Shier, W. Goddard,
    Chapter to Handbook of Discrete and Combinatorial Mathematics

45. 2017-3: Some remarks on the non-real roots of polynomials, Cubo  20  67--93  (2018)

46. 2017-2: Isogenous components of Jacobian surfaces,  Europ. Jour. Math. Vol. 6  1276--1302  (2020)

47. 2017-1:  Reduction of binary forms via the hyperbolic centroid, 
    Lobachevskii J. Math.  42  84--95  (2021) https://doi.org/10.1134/s199508022101011x 

48. 2016-6: On generalized superelliptic Riemann surfaces,
    Transformation Groups (2025)       https://arxiv.org/abs/1609.09576

49. 2016-5: Rational points in the moduli space of genus two,
    Contemp. Math., 703, 83--115  (2018)  https://doi.org/10.1090/conm/703/14132 

50. 2016-4: The Satake sextic in F-theory,  
    J. Geom. Phys.  120  290--305  (2017)   https://doi.org/10.1016/j.geomphys.2017.06.010 

51. 2016-3: A universal genus-two curve from Siegel modular forms,  
    SIGMA Symmetry Integrability Geom. Methods Appl.  13  Paper No. 089, 17  (2017) 

52. 2016-2: Self-inversive polynomials, curves, and codes,
    Contemp. Math., 703, AMS, 2018, 189–208. https://doi.org/10.1090/conm/703/14138  

53. 2016-1:  On the field of moduli of superelliptic curves,  
    Contemp. Math., 703, AMS, 2018, 47–62. https://doi.org/10.1090/conm/703/14130   

54. 2015-4: Theta functions of superelliptic curves,
    NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, 47–69.

55. 2015-3: Weight distributions, zeta functions and Riemann hypothesis for linear and algebraic geometry codes, 
    Albanian J. Math.  41  328--359  (2015)

56. 2015-2: Weierstrass points of superelliptic curves,  
    NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, 15–46.

57. 2015-1: The case for superelliptic curves,
    NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, 1–14.

58. 2014-2: Cyclic curves over the reals,  
    NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, 70–83.

59. 2014-1: Heights on algebraic curves, 
    NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, 137–175.

60. 2013-7: Bielliptic curves of genus 3 in hyperelliptic moduli,
    Appl. Algebra Engrg. Comm. Comput. 24  387--412 (2013) https://doi.org/10.1007/s00200-013-0209-9 

61. 2013-4: 2-Weierstrass points of genus 3 hyperelliptic curves with extra involutions,
    Comm. Algebra, 45  1879--1892  (2017). https://doi.org/10.1080/00927872.2016.1226861   

62. 2013-3: Decomposition of some Jacobian varieties of dimension 3
    Artificial Intelligence and Symbolic Computation. AISC 2014. Lect. Notes in Comp. Sci., vol 8884. Springer
    https://doi.org/10.1007/978-3-319-13770-4_17

63. 2013-2: Theta functions and symmetric weight enumerators for codes over imaginary quadratic fields
    Designs, Codes and Cryptography  76  217--235  (2015)   https://doi.org/10.1007/s10623-014-9943-7 

64. 2013-1: On Jacobians of curves with superelliptic components,  
    Contemp. Math., 629, American Mathematical Society, Providence, RI, 2014, 1–14.   

65. 2013-i: Computational algebraic geometry and its applications,  
    Appl. Algebra Engrg. Comm. Comput.  24  309--311  (2013)   https://doi.org/10.1007/s00200-013-0204-1

66. 2013-ii: Computational algebraic geometry,  
    J. Symbolic Comput.  57  1--2  (2013)   https://doi.org/10.1016/j.jsc.2013.05.001

67. 2012-2:  Genus two curves with many elliptic subcovers, 
    Comm. Algebra,  44  4450--4466  (2016)  https://doi.org/10.1080/00927872.2015.1027365

68. 2012-1: Some remarks on the hyperelliptic moduli of genus 3, 
    Comm. Algebra,   42  4110--4130  (2014)  https://doi.org/10.1080/00927872.2013.791305   

69. 2011-2: On superelliptic curves of level $n$ and their quotients,   Albanian J. Math.  5  115--137  (2011)

70. 2011-1: Quantum codes from superelliptic curves,   Albanian J. Math.  5  175--191  (2011)

71. 2010-1: The arithmetic of genus two curves,  
    NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 29, IOS Press, Amsterdam, 2011, 59–98.

72. 2009-1: Theta functions and algebraic curves with automorphisms, T. Shaska, S. Wijesiri, 
    NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 24, IOS Press, Amsterdam, 2009, 193–237.

73. 2008-5: On some applications of graphs to cryptography and turbocoding, T. Shaska, V. Ustimenko; 
    Albanian J. Math.  2  249--255  (2008)

74. 2008-4: Degree even coverings of elliptic curves by genus 2 curves,  Albanian J. Math.  2  241--248  (2008)

75. 2008-3: Determining equations of families of cyclic curves,  Albanian J. Math.  2  199--213  (2008)

76. 2008-2: On the homogeneous algebraic graphs of large girth and their applications,
    Linear Algebra Appl.  430  1826--1837  (2009)    https://doi.org/10.1016/j.laa.2008.08.023

77. 2008-1: Degree 4 coverings of elliptic curves by genus 2 curves, Albanian J. Math.  2  307--318  (2008)

78. 2007-5: Quantum Codes from Algebraic Curves with Automorphisms,
    Condensed Matter Physics 2008, Vol. 11, No 2(54), pp. 383–396

79. 2007-4: Some open problems in computational algebraic geometry, Albanian J. Math.  1  297--319  (2007)

80. 2007-3: Thetanulls of cyclic curves of small genus,  Albanian J. Math.  1  253--270  (2007)

81. 2007-2: Codes over rings of size {$p^2$} and lattices over imaginary quadratic fields, Finite Fields Appl.  16  75--87  (2010)   https://doi.org/10.1016/j.ffa.2010.01.005 

82. 2006-4: Subvarieties of the hyperelliptic moduli determined by group actions, Serdica Math. J.  32  355--374  (2006)

83. 2006-3: Codes over F_{p^2} and F_pxF_p, lattices, and theta functions,  Ser. Coding Theory Cryptol., 3, World Sci., 2007, 70–80. 

84. 2006-2: Codes over rings of size four, Hermitian lattices, and corresponding theta functions,
    Proc. Amer. Math. Soc.  136  849--857  (2008)    https://doi.org/10.1090/S0002-9939-07-09152-6   

85. 2006-1: On the automorphism groups of some AG-codes based on $C_{a,b}$ curves,
    Serdica J. Comput.  1  193--206  (2007)

86. 2005-4: A Maple package for hyperelliptic curves, T. Shaska, S. Zheng, 399--408  (2005)

87. 2005-3: Hyperelliptic curves of genus 3 with prescribed automorphism group, 
    Lecture Notes Ser. Comput., 13, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005, 109–123. 

88. 2005-2: Hyperelliptic curves with reduced automorphism group $A_5$, Appl. Algebra Engrg. Comm. Comput.  18  3--20  (2007)    https://doi.org/10.1007/s00200-006-0030-9 

89. 2005-1: Genus 2 curves that admit a degree 5 map to an elliptic curve,  Forum Math.  21  547--566  (2009)   https://doi.org/10.1515/FORUM.2009.027   

90. 2004-3: Invariants of binary forms, V. Krishnamoorthy, Dev. Math., 12, Springer, New York, 2005, 101–122. 

91. 2004-2:  Genus two curves covering elliptic curves: a computational approach,
    Lecture Notes Ser. Comput., 13, World Scientific Publishing Co. 2005, 206–231. 

92. 2004-1: Galois groups of prime degree polynomials with nonreal roots,
    Lecture Notes Ser. Comput., 13, World Scientific Publishing Co.  2005, 243–255. 

93. 2003-4: Computational algebra and algebraic curves, SIGSAM Bull. 37, 117--124  (2003)  https://doi.org/10.1145/968708.968713

94. 2003-3: Hyperelliptic curves with extra involutions,  LMS J. Comput. Math.  8  102--115  (2005)  https://doi.org/10.1112/S1461157000000917  

95. 2003-2: Some special families of hyperelliptic curves,  J. Algebra Appl.  3  75--89  (2004) https://doi.org/10.1142/S0219498804000745  

96. 2003-1: On the generic curve of genus 3,  Contemp. Math., Contemporary Math., 369, AMS,  Providence, RI, 2005 

97. 2002-3: Determining the automorphism group of a hyperelliptic curve,  (ISSAC 2003)
    Proceedings of International Symposium on Symbolic and Algebraic Computation, 248–254. (ACM), 2003

98. 2002-2: Computational aspects of hyperelliptic curves,
    Lecture Notes Ser. Comput., 10, World Scientific Publishing, 2003, 248–257. 

99. 2002-1: Genus 2 curves with (3,3)-split Jacobian and large automorphism group, (ANTS 2003)
    Lecture Notes in Comput. Sci., 2369, Springer-Verlag, Berlin, 2002, 205–218.   math/0201008

100. 2001-2: The locus of curves with prescribed automorphism group,
     Sürikaisekikenkyüsho K\B{o}kyüroku 112--141  (2002) math/0205314

101. 2001-1: Genus 2 fields with degree 3 elliptic subfields,
     Forum Math. 16  263--280  (2004)  https://doi.org/10.1515/form.2004.013  math/0109155

102. 2001-0: Curves of genus two covering elliptic curves, 
     Thesis (Ph.D.)--University of Florida pg.72 (2001).

103. 2000-2: Elliptic subfields and automorphisms of genus 2 function fields, 
     Algebra, arithmetic and Geometr, (Abhyankar's 70th birthday), 2000, 703–723, Springer, (2004)  math/0107142 

104. 2000-1: Curves of genus 2 with (n,n)-decomposable Jacobians,  
     J. Symbolic Comput. 31,  603--617, (2001). https://doi.org/10.1006/jsco.2001.0439   math/0312285