Goro Shimura
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Japanese mathematician
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Mathematics
Goro Shimura's Degrees
- PhD Mathematics Princeton University
- Masters Mathematics Princeton University
- Bachelors Mathematics University of Tokyo
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Why Is Goro Shimura Influential?
(Suggest an Edit or Addition)According to Wikipedia, Gorō Shimura was a Japanese mathematician and Michael Henry Strater Professor Emeritus of Mathematics at Princeton University who worked in number theory, automorphic forms, and arithmetic geometry. He was known for developing the theory of complex multiplication of abelian varieties and Shimura varieties, as well as posing the Taniyama–Shimura conjecture which ultimately led to the proof of Fermat's Last Theorem.
Goro Shimura's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Modular Forms of Half Integral Weight (1973) (1062)
- Introduction to the Arithmetic Theory of Automorphic Functions (1971) (974)
- On the Holomorphy of Certain Dirichlet Series (1975) (388)
- The special values of the zeta functions associated with cusp forms (1976) (372)
- Abelian Varieties with Complex Multiplication and Modular Functions (1997) (350)
- The special values of the zeta functions associated with Hilbert modular forms (1978) (314)
- ON ANALYTIC FAMILIES OF POLARIZED ABELIAN VARIETIES AND AUTOMORPHIC FUNCTIONS (1963) (290)
- Construction of Class Fields and Zeta Functions of Algebraic Curves (1967) (224)
- Confluent hypergeometric functions on tube domains (1982) (177)
- Sur les int\'egrales attach\'ees aux formes automorphes. (1959) (174)
- Euler Products and Eisenstein Series (1997) (172)
- On Canonical Models of Arithmetic Quotients of Bounded Symmetric Domains: II (1970) (153)
- On some arithmetic properties of modular forms of one and several variables (1975) (146)
- On Eisenstein series (1983) (144)
- On Elliptic Curves with Complex Multiplication as Factors of the Jacobians of Modular Function Fields (1971) (135)
- On the factors of the jacobian variety of a modular function field (1973) (125)
- ARITHMETIC OF UNITARY GROUPS (1964) (117)
- On the periods of modular forms (1977) (111)
- Arithmeticity in the Theory of Automorphic Forms (2000) (109)
- Correspondances modulaires et les fonctions ζ de courbes algebriques (1958) (108)
- V. The Zeta Function of an Abelian Variety with Complex Multiplication (1971) (94)
- Class Fields Over Real Quadratic Fields and Hecke Operators (1972) (90)
- ON MODULAR CORRESPONDENCES FOR SP(N, Z) AND THEIR CONGRUENCE RELATIONS. (1963) (87)
- On the real points of an arithmetic quotient of a bounded symmetric domain (1975) (87)
- On the Cohomology Groups Attached to Certain Vector Valued Differential Forms on the Product of the Upper Half Planes (1963) (86)
- Automorphic forms and the periods of abelian varieties (1979) (85)
- On the Field of Rationality for an Abelian Variety (1972) (84)
- REDUCTION OF ALGEBRAIC VARIETIES WITH RESPECT TO A DISCRETE VALUATION OF THE BASIC FIELD. (1955) (80)
- Arithmetic of alternating forms and quaternion hermitian forms (1963) (77)
- On certain reciprocity-laws for theta functions and modular forms (1978) (75)
- The Arithmetic of Certain Zeta Functions and Automorphic Forms on Orthogonal Groups (1980) (72)
- On Hilbert modular forms of half-integral weight (1987) (64)
- Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups (2004) (60)
- The representation of integers as sums of squares (2002) (58)
- Moduli and Fibre Systems of Abelian Varieties (1966) (56)
- On purely transcendental fields automorphic functions of several variable (1964) (56)
- Nearly holomorphic functions on hermitian symmetric spaces (1987) (55)
- On the zeta-functions of the algebraic curves uniformized by certain automorphic functions (1961) (55)
- On a class of nearly holomorphic automorphic forms (1986) (54)
- On Eisenstein series of half-integral weight (1985) (54)
- On the Field of Definition for a Field of Automorphic Functions: III (1964) (53)
- Algebraic Number Fields and Symplectic Discontinuous Groups (1967) (52)
- On Abelian Varieties with Complex Multiplication (1977) (52)
- On the Fourier coefficients of Hilbert modular forms of half-integral weight (1993) (52)
- Invariant differential operators on hermitian symmetric spaces (1990) (52)
- ON THE THEORY OF AUTOMORPHIC FUNCTIONS (1959) (52)
- On differential operators attached to certain representations of classical groups (1984) (51)
- A reciprocity law in non-solvable extensions. (1966) (50)
- ON DIRICHLET SERIES AND ABELIAN VARIETIES ATTACHED TO AUTOMORPHIC FORMS (1962) (48)
- The arithmetic of automorphic forms with respect to a unitary group (1978) (48)
- On the derivatives of theta functions and modular forms (1977) (47)
- On the Fourier coefficients of modular forms of several variables (2002) (43)
- Euler products and Fourier coefficients of automorphic forms on symplectic groups (1994) (41)
- Eisenstein series and zeta functions on symplectic groups (1995) (39)
- An exact mass formula for orthogonal groups (1999) (38)
- On the critical values of certain Dirichlet series and the periods of automorphic forms (1988) (38)
- Algebraic Relations Between Critical Values of Zeta Functions and Inner Products (1983) (38)
- Theta functions with complex multiplication (1976) (37)
- The critical values of certain zeta functions associated with modular forms of half-integral weight (1981) (36)
- Differential operators, holomorphic projection, and singular forms (1994) (36)
- ON THE TRANSFORMATION FORMULAS OF THETA SERIES (1993) (36)
- Discontinuous groups and abelian varieties (1967) (33)
- Arithmetic of differential operators on symmetric domains (1981) (33)
- On the Zeta Function of a Fibre Variety whose Fibres are Abelian Varieties (1965) (31)
- On vector differential forms attached to automorphic forms (1960) (31)
- On Certain Zeta Functions Attached to Two Hilbert Modular Forms: I. The Case of Hecke Characters (1981) (31)
- The special values of the zeta functions associated with Hilbert modular forms: Duke Mathematical Journal, 45 (1978), 637–679 (2003) (30)
- On certain zeta functions attached to two Hilbert modular forms II. The case of automorphic forms on a quaternion algebra (1981) (30)
- The periods of certain automorphic forms of arthmetic type (1982) (30)
- On the Eisenstein Series of Hilbert Modular Groups. (1985) (28)
- Elementary Dirichlet Series and Modular Forms (2007) (26)
- Some exact formulas on quaternion unitary groups (1999) (26)
- Automorphic Functions and Number Theory (1968) (26)
- Differential operators and the singular values of Eisenstein series (1984) (25)
- The number of representations of an integer by a quadratic form (1999) (23)
- NON-CRITICAL VALUES OF ADJOINT L-FUNCTIONS FOR SL(2) (23)
- Convergence of zeta functions on symplectic and metaplectic groups (1996) (22)
- Quadratic Diophantine Equations (2010) (21)
- On the class-fields obtained by complex multiplication of abelian varieties (1962) (19)
- Inhomogeneous quadratic forms and triangular numbers (2004) (17)
- Moduli of abelian varieties and number theory (2002) (16)
- Arithmetic of Quadratic Forms (2010) (16)
- Integer-valued quadratic forms and quadratic Diophantine equations. (2006) (15)
- Algebraic relations between critical values of zeta functions and inner products: American Journal of Mathematics, 105 (1983), 253–285 (2003) (15)
- On the fundamental periods of automorphic forms of arithmetic type (1990) (12)
- The critical values of certain Dirichlet series attached to Hilbert modular forms (1991) (12)
- Classification, construction, and similitudes of quadratic forms (2006) (11)
- On the trace formula for Hecke operators (1974) (11)
- Modular Forms: Basics and Beyond (2011) (11)
- On Specializations of Abelian Varieties (1959) (11)
- Generalized Bessel functions on symmetric spaces (1999) (11)
- Class-fields and Automorphic Functions (1964) (11)
- Quadratic Diophantine equations, the class number, and the mass formula (2006) (11)
- Zeta functions and Eisenstein series on metaplectic groups (1995) (10)
- Yutaka Taniyama and His Time Very Personal Recollections (1989) (9)
- An l-adic method in the theory of automorphic forms (1968) (8)
- Class fields over real quadratic fields in the theory of modular functions (1971) (7)
- Quadratic diophantine equations and orders in quaternion algebras (2006) (7)
- ON ARITHMETIC AUTOMORPHIC FUNCTIONS (1970) (6)
- Algebraic varieties without deformation and the Chow variety (1968) (6)
- The critical values of generalizations of the Hurwitz zeta function (2010) (6)
- Arithmeticity of automorphic forms (2010) (5)
- Arithmetic of Hermitian forms (2008) (5)
- Zeta functions and Eisenstein series on classical groups. (1997) (5)
- The Story of Imari: The Symbols and Mysteries of Antique Japanese Porcelain (2008) (5)
- The Map of My Life (2008) (5)
- The critical values of certain Dirichlet series (2008) (5)
- Fractional and Trigonometric Expressions for Matrices (1994) (5)
- Algebraic theory of quadratic forms, Clifford algebras, and spin groups (2004) (4)
- On Eisenstein series of half-integral weight: Duke Mathematical Journal, 52 (1985), 281–314 (2003) (4)
- Models of an abelian variety with complex multiplication over small fields (1982) (3)
- Local Representations of Galois Groups (1969) (3)
- The arithmetic of automorphic forms with respect to a unitary group: Annals of Mathematics, 107 (1978), 569–605 (2003) (3)
- A note on the normalization-theorem of an integral domain (2002) (2)
- On Hilbert modular forms of half-integral weight: Duke Mathematical Journal, 55 (1987), 765–838 (2003) (2)
- On the holomorphy of certain Dirichlet series: Proceedings of the London Mathematical Society, 3rd ser. 31 (1975), 79–98 (2002) (2)
- The periods of abelian varieties with complex multiplication and the spectral values of certain zeta functions (1980) (2)
- The arithmetic of certain zeta functions and automorphic forms on orthogonal groups: Annals of Mathematics, 111 (1980), 313–375 (2003) (2)
- Number fields and zeta functions associated with discontinuous groups and algebraic varieties: Proceedings of the International Congress of Mathematicians, Mascow, 1996, 100–107 (1967)* (2002) (2)
- On certain reciprocity-laws for theta functions and modular forms: Acta mathematica, 141 (1978), 35–71 (2003) (2)
- An ℓ-adic method in the theory of automorphic forms: The text of a lecture at the conference Automorphic functions for arithmetically defined groups,Oberwolfach, Germany, July28-August 3, 1968 (2002) (2)
- On certain zeta functions attached to two Hilbert modular forms: II. The case of automorphic forms on a quaternion algebra: Annals of Mathematics, 114 (1981), 569–607 (2003) (2)
- Corrections to “The special values of the zeta functions associated with Hilbert modular forms,” Vol. 45 (1978), 637–679 (1981) (1)
- On the critical values of certain Dirichlet series and the periods of automorphic forms: Inventiones mathematicae, 94 (1988), 245–305 (2003) (1)
- On differential operators attached to certain representations of classical groups: Inventiones mathematicae, 77 (1984), 463–488 (2003) (1)
- Classification of integer-valued symmetric forms (2008) (1)
- AN EXACT MASS FORMULA FOR ORTHOGONAL GROUPS GORO SHIMURA (1999) (1)
- The class-field-theoretical characterization of K’ (φ(z)) (1968) (1)
- Main theorems on Euler products, Eisenstein series, and the mass formula (Chapter IV) (1997) (1)
- The endomorphism-ring of an abelian variety; the field of moduli of an abelian variety with many complex multiplications (1968) (1)
- On some problems of algebraicity: Proceedings of the International Congress of Mathematicians, Helsinski, 1978 (1979), 373–379 (2003) (1)
- Arithmetic of differential operators on symmetric domains: Duke Mathematical Journal, 48 (1981), 813–843 (2003) (1)
- On the Eisenstein series of Hilbert modular groups: Revista mathemática Iberoamericana, 1 (1985), 1–42 (2003) (0)
- The periods of certain automorphic forms of arithmetic type: Journal of the Faculty of Science, University of Tokyo, Sec. IA, 28 (1982), 605–632 (2003) (0)
- The Arithmeticity of Critical Values of Dirichlet Series (2012) (0)
- [118] Response to Shimura’s Letter (2017) (0)
- Elliptic curves and the fundamental theorems of the classical theory of complex multiplication (1968) (0)
- Analytic continuation and near holomorphy of Eisenstein series of general types (2010) (0)
- Arithmeticity in the theory of automorphic forms, by Goro Shimura, Mathematical (2002) (0)
- Theta Functions and Factors of Automorphy (2012) (0)
- Confluent hypergeometric functions on tube domains: Mathematische Annalen, 260 (1982), 269–302 (2003) (0)
- Some old and recent arithmetical results concerning modular forms and related zeta functions (1992) (0)
- Automorphic forms and the periods of abelian varieties: Journal of the Mathematical Society of Japan, 31 (1979), 561–592 (2003) (0)
- Various Basic Theorems (2010) (0)
- Arithmeticity in the Theory of Automorphic Forms Goro Shimura (2007) (0)
- IV. Construction of Class Fields (1998) (0)
- Automorphic forms and families of abelian varieties (2010) (0)
- Further generalization and concluding remarks (1968) (0)
- III. Reduction of Constant Fields (1998) (0)
- Notation and Terminology (1998) (0)
- Nearly holomorphic functions on hermitian symmetric spaces: Mathematische Annalen, 278 (1987), 1–28 (2003) (0)
- Arithmetic of differential operators and nearly holomorphic functions (2010) (0)
- On a class of nearly holomorphic automorphic forms: Annals of Mathematics, 123 (1986), 347–406 (2003) (0)
- Critical Values of Dirichlet Series Associated with Imaginary Quadratic Fields (2007) (0)
- On Eisenstein series: Duke Mathematical Journal, 50 (1983), 417–476 (2003) (0)
- The zeta function of an algebraic variety and automorphic functions (2002) (0)
- Deeper Arithmetic of Quadratic Forms (2010) (0)
- Preface to Complex Multiplication of Abelian Varieties and Its Applications to Number Theory (1961) (1998) (0)
- VII. Theta Functions and Periods on Abelian Varieties (1998) (0)
- Preliminaries on Modular Forms and Dirichlet Series (2007) (0)
- The Quadratic Reciprocity Law (2010) (0)
- Zeta functions associated with Hecke eigenforms (2010) (0)
- A further method of constructing class fields (1968) (0)
- Euler products and Eisenstein series on Clifford groups (2004) (0)
- Typesetter's Correction to "On a Class of Nearly Holomorphic Automorphic Forms" (1986) (0)
- Unitary groups and theta functions: Proceedings of the International Symposium on Algebraic Number Theory, Kyoto 1976 (1977), 195–200 (2002) (0)
- The hasse zeta function of an algebraic curve (1968) (0)
- Erratum (2005) (0)
- Class fields over real quadratic fields in the theory of modular functions: In Several Complex VariablesII, Maryland 1970, Lecture notes in Mathematics 185 (1971), 169–188 (2002) (0)
- Quadratic forms, Clifford algebras, and spin groups over a local or global field (2004) (0)
- Abelian varieties and siegel modular functions (1968) (0)
- VI. Families of Abelian Varieties and Modular Functions (1998) (0)
- Differential operators and the singular values of Eisenstein series: Duke Mathematical Journal, 51 (1984), 261–329 (2003) (0)
- Arithmetic in an Algebraic Number Field (2010) (0)
- Euler products and Eisenstein series on orthogonal groups (2004) (0)
- The Case of Imaginary Quadratic Fields and Nearly Holomorphic Modular Forms (2007) (0)
- ON THE GLOBAL ROOT NUMBERS OF GL(n)× GL(m) (2006) (0)
- I. Preliminaries on Abelian Varieties (1998) (0)
- Eisenstein series of simpler types (2010) (0)
- Arithmeticity of the critical values of zeta functions and Eisenstein series of general types (2010) (0)
- The Correspondence between Forms of Integral and Half-integral Weight (2012) (0)
- Adelization of algebraic groups and automorphic forms (Chapter II) (1997) (0)
- Infinite galois extensions with l-adic representations (1968) (0)
- The Rationality and Eisenstein Series (2012) (0)
- Euler factors on local groups and Eisenstein series (Chapter III) (1997) (0)
- Models of an abelian variety with complex multiplication over small fields: Journal of number Theory, 15 (1982), 25–35 (2003) (0)
- On abelian varieties with complex multiplication: Proceedings of the London Mathematical Society, 3rd ser. 34 (1977), 65–86 (2002) (0)
- Algebraic and local theories of generalized unitary groups (Chapter I) (1997) (0)
- Groups and symmetric spaces over R (2004) (0)
- Automorphic functions on the upper half plane, especially modular functions (1968) (0)
- Critical Values of Dirichlet L-functions (2007) (0)
- Relation between the points of finite order on an elliptic curve and the modular functions of higher level (1968) (0)
- Algebras Over a Field (2010) (0)
- On complex multiplications (2002) (0)
- Some Remarks and Open Problems on the Woods Hole Fixed Point Formula (2016) (0)
- On the fields of definition for fields of automorphic functions (2002) (0)
- On certain zeta functions attached to two Hilbert modular forms: I. The case of Hecke characters: Annals of Mathematics, 114(1981), 127–164 (2003) (0)
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