Takashi Taniguchi

Japanese version

During Apr.2010 - Mar.2012, I am visiting Math. Department of Princeton University.
(Supported by JSPS Postdoctoral Fellowships for Research Abroad.)

Preprints

• [pdf](Dec, 2011) Orbital L-functions for the space of binary cubic forms, (with F. Thorne), arXiv:1112.5030, submitted.
• [pdf](Feb, 2011) Secondary terms in counting functions for cubic fields, (with F. Thorne), arXiv:1102.2914, submitted.
• [pdf](Apr, 2011) Relations among Dirichlet series whose coefficients are class numbers of binary cubic forms II, (with Y. Ohno), arXiv:1112.5029, submitted.
• [pdf](Aug, 2006) Distributions of discriminants of cubic algebras II, math.NT/0608658, revising.
• [pdf](Mar, 2006) Distributions of discriminants of cubic algebras, math.NT/0606109, revising.

Papers

• (In Japanese) [pdf] Introduction to higher composition laws (survey article), RIMS Kôkyûroku Bessatsu B25(2011), 211-254.
• Relations among Dirichlet series whose coefficients are class numbers of binary cubic forms, Amer. J. Math. 131-6(2009), 1525-1541 (with Y. Ohno and S. Wakatsuki).
• On parameterizations of rational orbits of forms of some prehomogeneous vector spaces, Manuscripta Math. 125-2(2008), 169-190.
• A mean value theorem for the square of class number times regulator of quadratic extensions, Ann. Inst. Fourier. 58-2(2008), 625-670.
• On proportional constants of the mean value of class numbers of quadratic extensions, Trans. Amer. Math. Soc., 359-11(2007), 5517-5524.
• On the zeta functions of prehomogeneous vector spaces for a pair of simple algebras, Ann. Inst. Fourier. 57-4(2007), 1331-1358.
• A mean value theorem for orders of degree zero divisor class groups of quadratic extensions over a function field, J. Number Theory, 109-2(2004), 197-239.

Talks

• February 8, 2012. Counting cubic fields and L-functions for the space of binary cubic forms, in Athens-Atlanta Number Theory Seminar, at University of Georgia.
• February 7, 2012. Counting cubic fields and L-functions for the space of binary cubic forms, in Number Theory Seminar, at University of South Carolina.

• December 1, 2011. A second main term for counting cubic fields, and biases in arithmetic progressions, in Princeton University / IAS Number Theory Seminar, at IAS.
• July 20, 2011. Secondary terms in counting functions for cubic fields, Explicit methods in number theory, at MFO, Oberwolfach.
• March 29, 2011. Secondary terms in counting functions for cubic fields, in Number Theory Seminar, at Rutgers University.

Workshops (co)organized

• April 9-11, 2012, Workshop on arithmetic geometry and related topics, at Kyoto University.
• Kobe Number Theory workshop (January 13-15, 2010).
• Ehime Number Theory workshop (February 17-20, 2009).

Workshops I'm interested in

• April 15-19, 2013, Combinatorics, Multiple Dirichlet series and Analytic Number Theory , at ICERM, Providence.
• July 17-23, 2011, Explicit methods in number theory, at MFO, Oberwolfach.
• June 13-17, 2011, The Cohen-Lenstra heuristics for class groups, at AIM, Palo Alto, California.
• March 21-25,2011, Workshop on Galois Representations and Automorphic Forms, at IAS, Princeton.
• Jan 31-Feb 4, 2011, Introductory Workshop: Arithmetic Statistics at MSRI, Berkeley.
• June 2-5, 2010. Number Theory and Representation Theory, at Harvard University.
• May 3-7, 2010. Second international workshop on zeta functions in algebra and geometry, in Spain.