Takashi Taniguchi

Japanese version

What's New

• I'm an editor of Kobe Journal of Mathematics.

Preprints

• Exponential sums over singular binary quartic forms and applications, (with Y. Ishitsuka, F. Thorne and S.Y. Xiao), arXiv:2404.00541.
• Periods modulo p of integer sequences associated with division polynomials of genus 2 curves, (with Y. Ishitsuka, T. Ito, T. Ohshita, and Y. Uchida ), arXiv:2310.01013.
• [PDF] (Aug, 2006) Distributions of discriminants of cubic algebras II, math.NT/0608658.
• [PDF] (Mar, 2006) Distributions of discriminants of cubic algebras, math.NT/0606109.

Papers

• Improved error estimates for the Davenport-Heilbronn theorems, Math. Ann., Online first. (with M. Bhargava and F. Thorne).
• Uniform bounds for lattice point counting and partial sums of zeta functions, Math. Z., 300 (2022), 2571-2590, (with David Lowry-Duda and F. Thorne).
• Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves, J. Amer. Math. Soc., 33 (2020), 1087-1099, (with M. Bhargava, A. Shankar, F. Thorne, J. Tsimerman, and Y. Zhao ).
• The local-global property for bitangents of plane quartics, JSIAM Letters, 12 (2020), 41-44, (with Y. Ishitsuka, T. Ito, T. Ohshita, and Y. Uchida ), arXiv:2002.10203.
• Levels of distribution for sieve problems in prehomogeneous vector spaces, Math. Ann., 376 (2020), 1537-1559, (with F. Thorne).
• Orbital exponential sums for prehomogeneous vector spaces, Amer. J. Math. 142-1(2020), 177-213, (with F. Thorne).
• Relations among Dirichlet series whose coefficients are class numbers of binary cubic forms II, Math. Res. Lett., 21-2(2014), 363-378, (with Y. Ohno).
• An error estimate for counting S_3-sextic number fields, Int. J. Number Theory, 10-4(2014), 935-948, (with F. Thorne).
• Orbital L-functions for the space of binary cubic forms, Canad. J. Math., 65-6(2013), 1320-1383 (with F. Thorne).
• Secondary terms in counting functions for cubic fields, Duke Math. J., 162-13(2013), 2451-2508, (with F. Thorne).
• Introduction to higher composition laws (in Japanese, survey article), RIMS Kôkyûroku Bessatsu B25(2011), 211-253.
• 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.

Proceedings

• Counting cubic fields (in Japanese), for the proceeding of Analytic Number Theory -- Arithmetic Properties of Transcendental Functions and their Applications, at RIMS. [PDF]

Visitors

• 2016-2017, Frank Thorne (South Carolina) / Stanley Yao Xiao (Oxford) / Yasuhiro Ishitsuka (Kyoto) /
• 2015-2016, Takahiro Tsushima (Chiba) / Tatsuya Oshita (Ehime) / Shunsuke Tsuchioka (Tokyo) / Masaki Watanabe (Tokyo) /
• 2014-2015, Andrew Booker (Bristol) / Frank Thorne (South Carolina) / Yasuhiro Ishitsuka (Kyoto) / Yayoi Nakamura (Kinki) / Yasuo Ohno (Tohoku)
• 2013-2014, Yasuhiro Ishitsuka (Kyoto) / Yu Yasufuku (Nihon) / John Miller (Rutgers) / Iwao Kimura (Toyama) / Arul Shankar (Harvard) / Gautam Chinta (CCNY) Minoru Hirose (Kyoto) / Nobuo Sato (Kyoto) / Miki Hirano (Ehime) / Yuichi Hirano (Tokyo)
• 2012-2013, Frank Thorne (South Carolina) / Keiju Sono (Tokyo) / Shuji Yamamoto (Keio) / Takehiko Yasuda (Osaka) / Kenichi Shimizu (Okayama) / Kohji Matsumoto (Nagoya) / Nobushige Kurokawa (Tokyo) / Maki Nakasuji (Sophia) / Shingo Saito (Kyushu)

Talks

• Octobor 31, 2018, Bounds on 2-torsion in class groups of number fields, Analytic Number Theory and Related Topics, at RIMS.
• December 13, 2017, Uniformity in Landau’s method and applications, Joetsu Number Theory Seminar, at Joetsu University of Education.
• November 20, 2017, Uniformity in Landau’s method and applications, Arithmetic Geometry and Related Topics, at Ehime University.
• June 16, 2017, On the numbers of cubic and quartic fields with almost prime discriminants, at Kyoto.
• June 9, 2017, Variants of Ohno-Nakagawa's dual identity, Kobe Number Theory Workshop 2017, at Kobe University.
• February 20, 2017, On the numbers of cubic and quartic fields with almost prime discriminants, The 10th Young Mathematicians Conference on Zeta Functions, at Nagoya University.
• July 25, 2016, Orbital exponential sums for prehomogeneous vector spaces, Whittaker Functions: Number Theory, Geometry and Physics, at BIRS.
• June 17, 2016, Exponential sums associated to prehomogeneous vector spaces, 2016 Seoul-Tokyo conference on Number Theory, at KIAS.
• January 25, 2016, Average rank of elliptic curves -Introduction to the work of Manjul Bhargava-, Arithmetic and Algebraic Geometry 2016, at University of Tokyo.
• November 9, 2015, Exponential sums for prehomogeneous vector spaces, Zeta Functions of Several Variables and Applications, at Nagoya University.
• September 5, 2014, Second order terms in some arithmetic functions, Prehomogeneous Vector Spaces and Related Topics (2014), at Rikkyo University.
• June 26, 2014, The zeta functions attached to prehomogeneous vector spaces, SMS2014 - Counting Arithmetic Objects, at CRM, University of Montreal.

Workshops (co)organized

• Kobe Number Theory Workshop 2017 (Jun 7-9, 2017).
• Kobe Number Theory Mini-Workshop (May 21-22, 2015).
• Nagoya Number Theory workshop, at Nagoya University (August 7-11, 2013).
• Workshop on arithmetic geometry and related topics, at Kyoto University (April 9-11, 2012).
• Kobe Number Theory workshop (January 13-15, 2010).
• Ehime Number Theory workshop (February 17-20, 2009).