Home Page for Haruzo HIDA

Haruzo HIDA
Distinguished Research Professor of Mathematics

Department of Mathematics, University of California, Los Angeles, California 90095-1555
Office Phone: (310) 206-3382
For e-mail address, see html

Link to "UCLA Number Theory Group web page": [html]

Forthcoming Conferences and Lectures:

Past Conferences/Workshops/Lectures (past 5 years):



Ph.D. Students

Math. genealogy of Hida [Mathematics Genealogy Project].
A brief [CV] and Mazur's account on Hida's work with Koji Doi [pdf] (see also the first page of [pdf]). Doi was an important figure in Hida's life as a mentor and also the one who introduced Hida Number Theory (as Hida did not have any under-graduate level knowledge of Mathematics until towards the end of his junior year of the undergraduate study when he somehow met Professor Doi in Kyoto). Doi passed away in summer 2016. Shimura momorial article [Notice AMS] (pdf file) and Taiwan Academia Sinica interview in Chinese [html] and its English translation [html].
Full List of Publication by H. Hida [pdf] and List of publications with review (subscription to MathSciNet necessary to view) [html]


These works are supported partially by various NSF grants and other sources if acknowledged.

H. Hida, Elementary Modular Iwasawa Theory, published in January 2022 in ``Series on Number Theory and its Application 16", World Scientific:
[World Scientific web site on this book] (preface and Chapter 1 available free posted on this page), a slide file for the summary of Chapter 4 [pdf]

H. Hida, Elliptic Curves and Arithmetic Invariants, Springer Monographs in Mathematics, 2013,
[Springer link] and [Springer web site of this book]

H. Hida, Geometric Modular Forms and Elliptic Curves, Second Expanded Edition, World Scientific Publishing Co., Singapore, 2011,
[World Scientific web site on this book] (Chapter 1 is free to download from this site)

H. Hida, Hilbert Modular Forms and Iwasawa Theory, Oxford Mathematical Monographs, Oxford University Press, 2006
[ Oxford web site on this book]. A list of misprints (as of 10/16/22): [pdf]

H. Hida, p-Adic Automorphic Forms on Shimura Varieties, Springer Monographs in Mathematics, 2004,
[Springer link], A list of misprints (as of 6/26/07): [pdf]

H. Hida, Modular Forms and Galois Cohomology, Cambridge Studies in advanced mathematics 69, 2000,
[ Cambridge University Press web site on this book ], A list of misprints (as of March 1, 2021): [pdf]

H. Hida, Geometric Modular Forms and Elliptic Curves, World Scientific Publishing Co., Singapore, 2000,
A list of misprints (as of September 16, 2011): [pdf]

H. Hida, Elementary Theory of L-functions and Eisenstein series, 1993, Cambridge University Press, Book [Cambridge web page]

p-Adic Aspects of Modular Forms, edited by Baskar Balasubramanyam, Haruzo Hida, A Raghuram, Jacques Tilouine, World Scientific Publishing Co., Singapore, 2016,
[World Scientific web site on this book] (Chapter 1 is free to download from this site)

Recent Publications in the last 7 years

(A link to older publications is at the end of this page.)
These works are supported partially by various NSF grants if acknowledged.

H. Hida, The universal ordinary deformation ring associated to a real quadratic field, preprint [Version of 3/10/21] (e=2 is stil an open question), published online in 2022, Math. Sciences, Proc. Indian Academy of Sci., reprint from Springer [pdf], reprint from Indian Academy [pdf], a Youtube link to a lecture at Columbia U. [11/19/20], a slide for a graduate student seminar lecture [pdf].

H. Hida, Local indecomposability via a presentation of the Hecke algebra, appendix to "Class groups and local indecomposability for non-CM forms" by F. Castella and C. Wang-Erickson, Journal of the European Mathematical Society, EMS site: [EMS] (entire paper), a preprint version: [ArXiv].

H. Hida, Cyclicity of adjoint Selmer groups and fundamental units, posted on Project Euclid: [pdf], preprint version of 12/28/20 [pdf], "Development of Iwasawa theory - The Centennial of K. Iwasawa's Birth" from Advanced Studies in Pure Mathematics 86 (2020), 351-411 (MSJ), a slide at Iwasawa 2017 [pdf].

H. Hida and J. Tilouine, Symmetric Power Congruence Ideals and Selmer Groups, preprint version of 10/12/18 [pdf], Journal of the Inst. of Math. Jussieu. 19 (2020), 1521-1572 , [html].

A. Burungale and H. Hida, p-rigidity and Iwasawa mu-invariants, Algebra & Number Theory 11 (2017), 1921-1951, a link to a reprint [html], a preprint version, [pdf].

H. Hida, Control of Lambda-adic Mordell-Weil groups, in "Elliptic Curves, Modular Forms and Iwasawa Theory" pp.253-294 (Coates 70th anniversary proceedings volume in "Proceedings in Mathematical Sciences 188, 2016" from Springer), a preprint version [pdf], Springer web page [htm] (ISBN 978-3-319-45032-2).

H. Hida, Arithmetic of adjoint L-values, Chapter 6 of p-Adic Aspects of Modular Forms, pp.185-236, World Scientific, 2016, Beijing lecture series web page, Lecture notes: No.1 [pdf], No.2 [pdf].

H. Hida, Growth of Hecke fields along a p-adic analytic family of modular forms, "Families of Automorphic Forms and the Trace Formula", pp.129-173, Simons Symposia, Springer, 2016, DOI 10.1007/978-3-319-41424-9-4, a reprint [pdf], Springer web site for the book [html].

A. Burungale and H. Hida, Andre-Oort conjecture and non-vanishing of central L-values over Hilbert class fields, Forum of Mathematics, Sigma 4 (2016), e20, 26 pp, DOI: [htm].

H. Hida, Limit Mordell-Weil groups and their p-adic closure, Extra Volume: Alexander S. Merkurjev's Sixtieth Birthday (2015) 221-264, Reprint file from Documenta Math: [pdf].

H. Hida and J. Tilouine, Big image of Galois representations and the congruence ideal, in the proceedings of the 2013 Bonn conference, Hausdorff trimester, LMS Lecture notes 420 (2015), 217-254, preprint, a version of 8/16/14 [pdf].

H. Hida, Big Galois representations and p-adic L-functions, Compositio Math. 151 (2015), 603-664, doi:10.1112/S0010437X14007684, link to the journal repreint file [pdf], a preprint version of 7/6/2014:[pdf], a slide for Paris talk [pdf].

Recent Preprints and Lecture Notes

(Last three years with some exception; a link to older notes is at the end of this page)

H. Hida, Non-vanishing of integrals of a mod p modular form, a preliminary version, preprint: [Version of 8/27/22] (a preliminary version), ICTS hybrid conference lectures: [1st lecture], [2nd lecture], [3rd lecture], [last lecture],

H. Hida, Adjoint L-value as a period integral and the mass formula of Siegel-Shimura, to appear in Kyoto Journal of Mathematics, preprint: [Version of 4/18/23] (a preliminary version), slide files [pdf] (11/15/21), [pdf] (4/14/23).

A. Burungale, H. Hida and Y. Tian, Horizontal variation of Tate--Shafarevich groups, a version of 12/31/17 [ArXiv],

H. Hida, Anticyclotomic cyclicity conjecture, preprint (a version of 6/23/17) [pdf], Rubinfest slide [pdf], a BIRS talk slide [pdf].

H. Hida, A series of lectures at Tata institute of fundamental research (Mumbai, India) 6/25/15-7/23/15, 1. Graduate students seminar [pdf], 2. Two lectures for limit Tate-Shafarevich groyps [pdf], [pdf], 3. Colloquium talk [pdf], 4. A lecture on limit Mordell-Weil groups [pdf].

H. Hida, Analytic variation of Tate-Shafarevich groups, preprint, a version of 11/2/17 [pdf].

H. Hida, On the rank of Mordell-Weil groups of abelian varieties of GL(2)-type, preprint, a version of 11/20/14 [pdf].

Older Publications

(More than 8 years old)

Older Lecture Notes

(More than 10 years old)
These works are supported partially by various NSF grants as acknowledged in each article.

UCLA Homepage
UCLA Math. Dept. Homepage