Publications and Preprints
[1]
Theta Functions and Division Points on Abelian Varieties of
Dimension Two
Thesis, MIT 1985. Advisor: Harold M. Stark
[2]
A generalization of Jacobi's derivative formula to dimension two
J. reine angew. Math.
392, 125-136 (1988).
pdf
[3] Coates-Wiles towers in dimension two
Math. Ann. 282, 645-666 (1988).
pdf
[4] On heterogeneous spaces
(with K. R. Coombes)
J. London Math. Soc. 40 (2) 385-397 (1989).
pdf
[5] Formal groups in genus two
J. reine. angew. Math. 411 96-121 (1990).
pdf
[6]
On a generalization of a formula of Eisenstein
Proc. London Math. Soc 3 121-132 (1991).
pdf
[7]
Small solutions to a given quadratic form with a variable modulus
J. Number Theory 42 No. 1, 57-60 (1992).
pdf
[8]
Computing the Mordell--Weil rank of Jacobians of curves of genus
2
(with D. M. Gordon)
Trans. Amer. Math. Soc. 337 No. 2, 807-824 (1993).
pdf
[9]
Integer points on curves of genus 2 and their Jacobians
Trans. Amer. Math. Soc. 344 No. 1, 79-100 (1994).
pdf
[10]
A curve for which Coleman's effective Chabouty bound is sharp
Proc. Amer. Math. Soc. 122 No. 1, 317-319 (1994).
pdf
[11]
Units from 3- and 4-torsion on Jacobians of curves of genus 2
Comp. Math. 94 311-320 (1994).
pdf
[12]
Formal groups of twisted multiplicative groups and L-series
(with N. Childress)
Proc. Symp. Pure Math. 58.2 89-102 (1995).
pdf
[13]
A proof of quintic reciprocity using the arithmetic of
y^2=x^5+1/4
Acta Arith. LXXV.4 321-337 (1996).
pdf
[14]
Sequences of fields with many solutions to the unit equation
Rocky Mount. J. Math. 26 1017-1029 (1996).
pdf
[15]
Units from 5-torsion on the Jacobian of y^2=x^5+1/4 and the
conjectures of Stark and Rubin
J. Number Theory 77 227-251 (1999).
pdf
[16]
A public key cryptosystem based on sparse polynomials
(with K. Krastev, D. Lieman and I. Shparlinski)
Coding Theory, Cryptography, and Related Areas (J. Buchmann, T. Hoeholdt,
H. Stichtenoth,
H. Tapia-Recillas, Eds.), 1999.
pdf
[17]
A formula for the number of elliptic curves with exceptional primes
Compositio Math. 122 151-164 (2000).
pdf
[18]
Examples of torsion points on genus 2 curves
(with J. Boxall)
Trans. AMS 352 No. 10, 4533-4555 (2000).
pdf
[19]
Five-torsion points on curves of genus two
(with J. Boxall and F. Leprevost)
J. London Math. Soc (2)
64 29-43 (2001)
pdf
[20]
An explicit theorem of the square for hyperelliptic Jacobians
(with J. Arledge)
Michigan Math. J. 49 485-492 (2001).
pdf
[21]
On Gunning's prime form in genus 2
Canad. Math. Bull. 45 89-96 (2002).
pdf
[22]
Some product formulas for theta functions in one and two variables
Acta Arithmetica 102 223-238 (2002).
pdf
[23]
Theta functions and singular torsion on elliptic curves
(with J. Boxall)
in Number Theory for the Millenium I, A K Peters, Natick (2002) 111-126.
pdf
[24]
Singular torsion on elliptic curves
(with J. Boxall)
Math. Research Letters 10 847-866 (2003).
pdf
[25]
Torsion on theta divisors of hyperelliptic Fermat Jacobians
Compositio Mathematica 140 1432-1438 (2004).
pdf
[26]
Cuspidal torsion packets on hyperelliptic Fermat quotients
(with D. Shaulis)
J. Théor. Nombres Bordeaux 16 577-585 (2004).
pdf
[27]
Geometric proofs of reciprocity laws
J. Reine Angew. Math. 586 91-124 (2005).
pdf
[28]
Weight enumerators and a MacWilliams-type identity for space-time
rank codes over finite fields
(with M. Varanasi)
Proceedings of the 43rd Annual Allerton Conference on Communication,
Control, and Computing
2137-2146 (2005)
pdf
[29]
Some remarks on almost rational torsion points
(with J. Boxall)
J. Théor. Nombres Bordeaux 18 13-28 (2006)
pdf
[30]
Duality theory for space-time codes over finite fields
(with M. Varanasi)
Advances in the Mathematics of Communications
2 35-54 (2008)
pdf
[31]
The equivalence of space-time codes and codes
over finite fields and Galois rings
(with M. Varanasi)
Advances in Mathematics of Communications
2
131-145 (2008)
pdf
[32]
Space-time codes and non-associative division algebras arising from elliptic curves
(with A. Deajim)
Contemporary Mathematics
463 29-44
(2008)
pdf
[33]
One-parameter families of elliptic curves over Q with maximal
Galois representations
(with A. Cojocaru and N. Jones)
Proceedings of the London Math. Soc.
103 654-675 (2011)
pdf
[34]
On the classification of 3-dimensional
non-associative division algebras over p-adic
fields
(with A. Deajim)
Journal de Theorie des Nombres de Bordeaux
23 329-346 (2011)
pdf
[35]
Integral division points on curves
(with S. Ih)
Compositio Math.
149 2011-2035 (2013)
pdf
[36]
On an analogue of the Lutz-Nagell Theorem for hyperelliptic curves
Journal of Number Theory
133 963-969 (2013)
pdf
[37]
The quadratic Gauss Sum redux
Amer. Math. Monthly
121
145-149 (2014)
pdf
[38]
Higher Genus Universally Decodable Matrices (UDMG)
(with S. Limburg, M. Varanasi)
Advances in the Mathematics of Communications
8
257-270 (2014)
.pdf
[39]
Feasibility of Single-Beam Interference Alignment in Multi-Carrier Interference Channels
(with M. Varanasi)
IEEE Transactions on Information Theory
63
7352-7357 (2017)
.pdf
[40]
A generalization of Jacobi's derivative formula to dimension two, II.
Acta Arithmetica
190.4
403-420 (2019)
.pdf
[41]
A higher-order generalization of Jacobi's derivative formula and its algebraic geometric analogue
Journal de Theorie des Nombres de Bordeaux
33
361-386 (2021)
.pdf
[42]
On the universal p-adic sigma and Weierstrass zeta functions
(with C. Blakestad)
J. Number Theory
249
348-376 (2023)
.pdf
[43]
Differential Codes on Higher Dimensional Varieties Via Grothendieck's Residue Symbol
(with John D. Massman, III, Srimathy Srinivasan)
submitted
.pdf
In Other Fields
Modeling Human Health Behavior with a New Index That Measures Connectivity
(with Bernstein, Steven; Li, Fangyong; Abujarad, Fuad; D'Onofrio, Gail; Dziura, James)
Preventive Medicine Reports
33
102172
.pdf
All-In University (with Robert Tubbs), in
Transformational Change Efforts: Student Engagement in Mathematics through an Institutional Network for Active Learning
(edited by Wendy M. Smith, Matthew Voijt, April Strom, David C. Webb, W. Gary Martin, AMS/CBMS (2021).
Culture and Equity (with Matthew Voijt, Wendy M. Smith, Nancy Kress and April Strom), in
Transformational Change Efforts: Student Engagement in Mathematics through an Institutional Network for Active Learning
(edited by Wendy M. Smith, Matthew Voijt, April Strom, David C. Webb, W. Gary Martin, AMS/CBMS (2021).
Sustainability (with Molly Williams, W. Gary Martin, Michael E. O'Sullivan), in
Transformational Change Efforts: Student Engagement in Mathematics through an Institutional Network for Active Learning
(edited by Wendy M. Smith, Matthew Voijt, April Strom, David C. Webb, W. Gary Martin, AMS/CBMS (2021).
An Ethical Opening for Higher Ed Institutions
(with M. Meaney)
Inside Higher Education (August 27, 2020)
here
Babe Ruth, sabermetrics, and baseball's politics of greatness
(with L. Cassuto)
The Cambridge Companion to Baseball
Cambridge University Press (2011)
ad
How do organisms respond to competing energetic requirements? The working
energy/take-home energy hypothesis.
(with K. Laland and R. Levin)
Integrative and Comparative
Biology
44(6) 719 (2004)
Calculus, the paper (submitted)