Updated on 2026/04/27
Graduate School of Science Department of Mathematics
Professor 2025.04 - Now
School of Science Department of Mathematics
Professor 2025.04 - Now
PhD （ Others ） ( California Institute of Technology )
Natural Science / Algebra / Number Theory, Automorphic Forms
My primary interests lie at the intersection of number theory and algebra, particularly understanding and discovering algebraic structures in arithmetic, and connecting different types of objects (modular forms, automorphic representations, representations of p-adic groups, L-functions, quaternion algebras, algebraic groups, elliptic curves, genus 2 curves, ...). Much of this is done with group theory, representation theory, harmonic analysis, and/or computations. I've also done a bit with graph theory, combinatorial optimization and spectral geometry.
University of Oklahoma
2007 - 2025
Columbia University
2004 - 2007
Distribution of local signs of modular forms and murmurations of Fourier coefficients
Kimball Martin
Mathematika 2025.07
Moduli for rational genus 2 curves with real multiplication for discriminant 5
Alex Cowan, Kimball Martin
Journal de théorie des nombres de Bordeaux 2024.11（ ISSN:2118-8572 ）
Mass formulas and Eisenstein congruences in higher rank
Kimball Martin, Satoshi Wakatsuki
Journal of Number Theory 2024.04（ ISSN:0022-314X ）
Local conductor bounds for modular abelian varieties
Kimball Martin
Acta Arithmetica 2024（ ISSN:0065-1036 ）
Root number bias for newforms
Martin, Kimball
Proc. Amer. Math. Soc. 2023（ ISSN:0002-9939 ）
Refined Goldbach conjectures with primes in progressions
Martin, Kimball
Exp. Math. 2022（ ISSN:1058-6458 ）
Exact double averages of twisted $L$-values
Martin, Kimball
Math. Z. 2022（ ISSN:0025-5874 ）
Rank bias for elliptic curves mod $p$
Martin, Kimball, Pharis, Thomas
Involve 2022（ ISSN:1944-4176 ）
An on-average Maeda-type conjecture in the level aspect
Martin, Kimball
Proc. Amer. Math. Soc. 2021（ ISSN:0002-9939 ）
The basis problem revisited
Martin, Kimball
Trans. Amer. Math. Soc. 2020（ ISSN:0002-9947 ）
Zeroes of quaternionic modular forms and central $L$-values
Martin, Kimball, Wiebe, Jordan
J. Number Theory 2020（ ISSN:0022-314X ）
Rationality of Darmon points over genus fields of non-maximal orders
Longo, Matteo, Martin, Kimball, Hu, Yan
Ann. Math. Qué. 2020（ ISSN:2195-4755 ）
Congruences for modular forms mod 2 and quaternionic $S$-ideal classes
Martin, Kimball
Canad. J. Math. 2018（ ISSN:0008-414X ）
Periods and nonvanishing of central $L$-values for $GL(2n)$
Feigon, Brooke, Martin, Kimball, Whitehouse, David
Israel J. Math. 2018（ ISSN:0021-2172 ）
Refined dimensions of cusp forms, and equidistribution and bias of signs
Martin, Kimball
J. Number Theory 2018（ ISSN:0022-314X ）
The Jacquet-Langlands correspondence, Eisenstein congruences, and integral $L$-values in weight 2
Martin, Kimball
Math. Res. Lett. 2017（ ISSN:1073-2780 ）
Test vectors and central $L$-values for $GL(2)$
File, Daniel, Martin, Kimball, Pitale, Ameya
Algebra Number Theory 2017（ ISSN:1937-0652 ）
Distinguishing finite group characters and refined local-global phenomena
Martin, Kimball, Walji, Nahid
Acta Arith. 2017（ ISSN:0065-1036 ）
A comparison of automorphic and Artin $L$-series of $GL(2)$-type agreeing at degree one primes
Martin, Kimball, Ramakrishnan, Dinakar
Advances in the theory of automorphic forms and their $L$-functions 2016（ ISBN:9781470417093 ）
Distinguishing graphs with zeta functions and generalized spectra
Durfee, Christina, Martin, Kimball
Linear Algebra Appl. 2015（ ISSN:0024-3795 ）
How often should you clean your room?
Martin, Kimball, Shankar, Krishnan
Discrete Math. Theor. Comput. Sci. 2015（ ISSN:1365-8050 ）
Local root numbers, Bessel models, and a conjecture of Guo and Jacquet
Furusawa, Masaaki, Martin, Kimball
J. Number Theory 2015（ ISSN:0022-314X ）
On central critical values of the degree four $L$-functions for GSp(4): a simple trace formula
Furusawa, Masaaki, Martin, Kimball
Math. Z. 2014（ ISSN:0025-5874 ）
On central critical values of the degree four $L$-functions for $GSp(4)$: the fundamental lemma. III
Furusawa, Masaaki, Martin, Kimball, Shalika, Joseph A.
Mem. Amer. Math. Soc. 2013（ ISSN:0065-9266 ） （ ISBN:9780821887424 ）
A relative trace formula for a compact Riemann surface
Martin, Kimball, McKee, Mark, Wambach, Eric
Int. J. Number Theory 2011（ ISSN:1793-0421 ）
Nonunique factorization and principalization in number fields
Martin, Kimball
Proc. Amer. Math. Soc. 2011（ ISSN:0002-9939 ）
On central critical values of the degree four $L$-functions for $GSp(4)$: the fundamental lemma, II
Furusawa, Masaaki, Martin, Kimball
Amer. J. Math. 2011（ ISSN:0002-9327 ）
Central $L$-values and toric periods for $GL(2)$
Martin, Kimball, Whitehouse, David
Int. Math. Res. Not. IMRN 2009（ ISSN:1073-7928 ）
Shalika periods on $GL_2(D)$ and $GL_4$
Jacquet, Hervé, Martin, Kimball
Pacific J. Math. 2007（ ISSN:0030-8730 ）
Modularity of hypertetrahedral representations
Martin, Kimball
C. R. Math. Acad. Sci. Paris 2004（ ISSN:1631-073X ）
Four-dimensional Galois representations of solvable type and automorphic forms
Martin, Kimball
2004 （ ISBN:9780496113958 ）
A symplectic case of Artin's conjecture
Martin, Kimball
Math. Res. Lett. 2003（ ISSN:1073-2780 ）
Central values of L-functions and quaternion algebras
Grant-in-Aid for Research Activity Start-up 2026
Central values of L-functions and quaternion algebras
Grant-in-Aid for Research Activity Start-up 2025.07
数理構造論演習1
2025 Intensive lecture Graduate school
数理構造論演習2
2025 Intensive lecture Graduate school
海外特別研究1
2025 Intensive lecture Graduate school
海外特別研究2
2025 Intensive lecture Graduate school
数学特別研究1B
2025 Intensive lecture Graduate school
数学特別研究2B
2025 Intensive lecture Graduate school
サイエンスフロンティアA（数学）
2025 Intensive lecture Graduate school
サイエンスフロンティアB（数学）
2025 Intensive lecture Graduate school
海外特別研究3
2025 Intensive lecture Graduate school
海外特別研究3
2025 Intensive lecture Graduate school
海外特別研究4
2025 Intensive lecture Graduate school
海外特別研究5
2025 Intensive lecture Graduate school
数学特別研究3B
2025 Intensive lecture Graduate school
数学特別研究4B
2025 Intensive lecture Graduate school
数学特別研究5B
2025 Intensive lecture Graduate school
数理構造論ゼミナール
2025 Intensive lecture Graduate school
数学卒業研究B
2025 Intensive lecture Undergraduate
数学特別研究3A
2025 Intensive lecture Graduate school
数学特別研究4A
2025 Intensive lecture Graduate school
数学特別研究5A
2025 Intensive lecture Graduate school
数学特別研究1A
2025 Intensive lecture Graduate school
数学特別研究2A
2025 Intensive lecture Graduate school
数学卒業研究A
2025 Intensive lecture Undergraduate