Gerhard Frey | Academic Influence

Gerhard Frey's AcademicInfluence.com Rankings

Gerhard Frey

Mathematics

#85

World Rank

#238

Historical Rank

Measure Theory

#3933

World Rank

#4635

Historical Rank

mathematics Degrees

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Mathematics

Gerhard Frey's Degrees

PhD Mathematics University of Göttingen

Why Is Gerhard Frey Influential?

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According to Wikipedia, Gerhard Frey is a German mathematician, known for his work in number theory. Following an original idea of Hellegouarch, he developed the notion of Frey–Hellegouarch curves, a construction of an elliptic curve from a purported solution to the Fermat equation, that is central to Wiles's proof of Fermat's Last Theorem.

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Gerhard Frey'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

Handbook of Elliptic and Hyperelliptic Curve Cryptography (2005) (1154)
A remark concerning m -divisibility and the discrete logarithm in the divisor class group of curves (1994) (675)
The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems (1999) (265)
Complex Multiplication (2005) (235)
On Artin's conjecture for odd 2-dimensional representations (1994) (118)
Applications of Arithmetical Geometry to Cryptographic Constructions (2001) (97)
Curves with infinitely many points of fixed degree (1994) (88)
Curves of genus 2 covering elliptic curves and an arithmetical application (1991) (82)
Approximation Theory and the Rank of Abelian Varieties Over Large Algebraic Fields (1974) (79)
Links between solutions of A−B=C and elliptic curves (1989) (60)
Arithmetic of Modular Curves and Applications (1997) (43)
On Ternary Equations of Fermat Type and Relations with Elliptic Curves (1997) (37)
On the different of abelian extensions of global fields (1992) (33)
Elliptic curves and solutions of A-B=C (1987) (26)
Curves with infinite K-rational geometric fundamental group (2001) (25)
Some remarks concerning points of finite order on elliptic curves over global fields (1977) (25)
Pseudo algebraically closed fields with non-Archimedean real valuations (1973) (24)
On the Selmer Group of Twists of Elliptic Curves with Q-Rational Torsion Points (1988) (24)
Properties of twists of elliptic curves. (1990) (23)
Background on Pairings (2005) (22)
Fast Bilinear Maps from the Tate-Lichtenbaum Pairing on Hyperelliptic Curves (2006) (21)
Curves of genus 2 with elliptic differentials and associated Hurwitz spaces (2009) (18)
Galois representations of octahedral type and 2-coverings of elliptic curves (1991) (17)
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition (2012) (17)
Computation of the 2-rank of pure cubic fields (1978) (15)
Construction and arithmetical applications of modular forms of low weight (1994) (15)
MATHEMATICAL BACKGROUND OF PUBLIC KEY CRYPTOGRAPHY (2005) (15)
Classically Projective Groups and Pseudo Classically Closed Elds (14)
Varieties over Special Fields (2005) (11)
On the structure of the class group of a function field (1979) (10)
Projective p-adic representations of the K-rational geometric fundamental group (2001) (8)
Correspondences on Hyperelliptic Curves and Applications to the Discrete Logarithm (2011) (7)
Implementation of Pairings (2005) (7)
Background on Curves and Jacobians (2005) (7)
A remark about isogenies of elliptic curves over quadratic fields (1986) (7)
The Way to the Proof of Fermat’s Last Theorem (2009) (7)
Horizontal isogeny theorems (2002) (7)
A relation between the value of theL-series of the curve:y2=x3−k3 ins=1 and its Selmer group (1985) (7)
On the Relation between Brauer Groups and Discrete Logarithms (2005) (7)
The strong Lefschetz principle in algebraic geometry (1986) (6)
The Arithmetic Behind Cryptography (2010) (5)
On using expansions to the base of −2 (2003) (5)
Discrete Logarithms, Duality, and Arithmetic in Brauer Groups (2008) (5)
Non-constant curves of genus 2 with infinite pro-Galois covers (2003) (5)
Curves, Jacobians, and cryptography (2018) (4)
Galois representations attached to elliptic curves and diophantine problems (2001) (4)
Transfer of Discrete Logarithms (2005) (3)
On Bilinear Structures on Divisor Class Groups (2009) (2)
Normal forms of hyperelliptic curves of genus 3 (2015) (2)
Relations between arithmetic geometry and public key cryptography (2010) (2)
Non-constant genus 2 curves with pro-Galois covers (2003) (2)
[From animal automatons to scientific questioning--reflections on the development of veterinary medicine in the 18th century]. (1996) (1)
Background on curves and Jacobians (Chapter 4) (2006) (1)
Did the Plague Impact Sub-Saharan Africa before 1899? (2012) (1)
Selected papers on epistemology and physics (1976) (1)
Varieties over special fields (Chapter 5) (2006) (1)
Algebraic Realizations of DL Systems (2005) (1)
The way to the proof of Fermat's theorem (1997) (1)
Change attachment for messeinsatztraeger in probes (1981) (0)
Abstract for Poster Session at Ants 2006, Poster Title: Efficient Arithmetic on Binary Hyperelliptic Curves (0)
Transfer of discrete logarithmics (Chapter 22) (2006) (0)
Titles and Abstracts (2012) (0)
Normal forms of hyperelliptic curves of genus 3 (2015) (0)
Logic as Empirical Science (1965) (0)
Calculating Really Big Cyclotomic Polynomials (2008) (0)
Facility for irradiation of products fliessfaehigen (1974) (0)
The Inobjectivity of the Philosophy of Existence (1972) (0)
Non standard arithmetic and application to height functions (1981) (0)
Schlick’s Konstatierungen Viewed As Special Case of General Theoretical Principles of Scientific Inquiry (1982) (0)
Scientific Knowledge about Nature and Reality (1968) (0)
Quadrate in Qp (1984) (0)
Background on Weil Descent (2005) (0)
Forschungsseminar on Quaternion Algebras (2008) (0)
MATHEMATICAL BACKGROUND OF PUBLIC KEY CRYPTOGRAPHY by Gerhard Frey (2005) (0)
Algebraic realizations of DL systems (Chapter 23) (2006) (0)
Cyclic isogenies and nonstandard arithmetic (1980) (0)
Algebra and number theory : proceedings of a conference held at the Institute of Experimental Mathematics, University of Essen (Germany), December 2-4, 1992 (1994) (0)
Brauer Groups in Cryptography 2 1 Discrete Logarithms in Ideal Class Groups (2005) (0)
Isogenies in Theory and Praxis (2014) (0)
Background on Weil descent (Chapter 7) (2006) (0)
On the number of elliptic curves with cm over large algebraic fields (2005) (0)

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