Paulo Ribenboim | Academic Influence

Paulo Ribenboim's AcademicInfluence.com Rankings

Paulo Ribenboim

Mathematics

#1082

World Rank

#1841

Historical Rank

Number Theory

#30

World Rank

#49

Historical Rank

Measure Theory

#1704

World Rank

#2095

Historical Rank

mathematics Degrees

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Mathematics

Paulo Ribenboim's Degrees

PhD Mathematics University of São Paulo

Why Is Paulo Ribenboim Influential?

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According to Wikipedia, Paulo Ribenboim is a Brazilian-Canadian mathematician who specializes in number theory. Biography Ribenboim was born into a Jewish family in Recife, Brazil. He received his BSc in mathematics from the University of São Paulo in 1948, and won a fellowship to study with Jean Dieudonné in France at the University of Nancy in the early 1950s, where he became a close friend of Alexander Grothendieck. He has contributed to the theory of ideals and of valuations.

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Paulo Ribenboim'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

The new book of prime number records (1996) (504)
The Book of Prime Number Records (1988) (338)
13 lectures on Fermat's last theorem (1981) (267)
Théorie des valuations (1964) (220)
Collected Papers, Volume 1+2 (1999) (177)
Classical Theory Of Algebraic Numbers (2001) (159)
The Little Book of Bigger Primes (2004) (143)
The little book of big primes (1991) (138)
Rings and modules (1969) (113)
The theory of classical valuations (1999) (112)
Fermat's last theorem for amateurs (1999) (108)
Noetherian rings of generalized power series (1992) (105)
Semisimple Rings and Von Neumann Regular Rings of Generalized Power Series (1997) (93)
Fields: Algebraically closed and others (1992) (84)
My Numbers, My Friends: Popular Lectures on Number Theory (2000) (74)
Rings of Generalized Power Series: II: Units and Zero-Divisors (1994) (67)
The Square Terms in Lucas Sequences (1996) (65)
Catalan's conjecture (1996) (65)
Fields of generalized power series (1990) (62)
Fixed points, combs and generalized power series (1993) (62)
Special Properties of Generalized Power Series (1995) (61)
Ultrametric Spaces and Logic Programming (2000) (59)
Generalized ultrametric spaces I (1996) (56)
Rings of generalized power series: Nilpotent elements (1991) (52)
Generalized ultrametric spaces II (1996) (49)
Catalan's conjecture : are 8 and 9 the only consecutive powers? (1994) (43)
The new theory of ultrametric spaces (1996) (39)
The Common Point Theorem for Ultrametric Spaces (1998) (31)
Generalized Power Series Rings (1990) (24)
Equations in groups, with special emphasis on localization and torsion - II (1987) (23)
Some Examples of Valued Fields (1995) (21)
The ABC Conjecture and the Powerful Part of Terms in Binary Recurring Sequences (1999) (19)
The Fibonacci numbers and the Arctic Ocean (1995) (17)
Class Numbers of Quadratic Fields (2001) (17)
Higher derivations of rings (1969) (16)
Square-Classes in Lucas Sequences Having Odd Parameters (1998) (16)
Logic programming and ultrametric spaces (1999) (15)
Squares in Lucas sequenceshaving an even first parameter (1998) (15)
Differential equations over valued fields (and more) (2004) (14)
An Algorithm to Determine the Points with Integral Coordinates in Certain Elliptic Curves (1999) (13)
Algebraic structures on graphs (1983) (13)
Equivalence relations and spherically complete ultrametric spaces (1995) (12)
An elementary note on group-rings. (1970) (12)
Ultrametric Dynamics (2012) (11)
The approximation to a fixed point (2013) (10)
Collected papers of Trygve Nagell (2002) (9)
Linear representation of finite groups : lecture notes (1966) (9)
On Lucas sequence terms of the form kx2 (2001) (9)
Polynomials whose values are powers. (1974) (8)
The Absolute Galois Group of a Rational Function Field in Characteristic Zero is a Semi-Direct Product (1984) (8)
Pell numbers, squares and cubes (1999) (7)
An existence theorem for fields with Krull valuations (1962) (7)
Ordering the set of antichains of an ordered set (1995) (7)
On the completion of a valuation ring (1964) (7)
Prime Number Records (1994) (6)
Functions, limits, and continuity (1964) (6)
Homogeneous Ultrametric Spaces (1996) (6)
On ordered modules. (1967) (6)
Fermat's equation for matrices or quaternions over $q$-adic fields (2004) (6)
Ordered Rings of Generalized Power Series (1993) (5)
The immersion of ultrametric spaces into Hahn spaces (2010) (5)
A short note on henselian fields (1967) (5)
Prime ideals in polynomial rings (1981) (5)
Square classes of Lucas sequences (1991) (5)
On the extension of orders in ordered modules (1970) (5)
Pfister's Dimension and the Level of Fields. (1974) (4)
How to Recognize Whether a Natural Number is a Prime (1996) (4)
Collected papers of Wilhelm Ljunggren (2003) (4)
Are There Functions That Generate Prime Numbers (1997) (4)
Active sums of groups. (1981) (4)
The Riemann-Roch Theorem For Algebraic Curves (1965) (4)
Extension of Hironaka's standard basis theorem for generalized power series (1993) (4)
Remarks on existentially closed fields and diophantine equations (1984) (4)
The (ABC) Conjecture and the radical index of integers (2001) (3)
An application of tarskis principle to absolute Galois groups of function fields (1987) (3)
Active sums of profinite groups (1983) (3)
Binary recurring sequences and powers, I (1999) (3)
Proceedings of the Queen's Number Theory Conference, 1979 (1980) (3)
CHAINING PARTIALLY ORDERED SETS (1994) (3)
Extension of Ideals (2001) (2)
Collected papers of Paulo Ribenboim (1997) (2)
On the extension of orders in ordered modules: Corrigenda (1971) (2)
A General Hensel's Lemma (2000) (2)
The terms Cx^h (h>=3) in Lucas sequences (2003) (2)
Power series over mori domains (1988) (2)
The skeleton, Hahn spaces and immediate extensions of ultrametric spaces (1995) (2)
Some Criteria for the First Case of Fermat's Last Theorem (1978) (2)
Localization of profinite groups (1984) (2)
Wolfgang Krull : gesammelte Abhandlungen = collected papers (1999) (2)
Collected papers of Pierre Samuel (1995) (2)
Variations and Fugue on a Theme (1979) (2)
Fff: (favorite Fibonacci Flowers) (2009) (2)
The Dedekind Zeta-Function (2001) (2)
Class Number of Cyclotomic Fields (2001) (2)
Cohomology and Homology of Pairs of Preshaves. (1968) (2)
Valuations and lengths of constructible modules. (1976) (1)
Derivations d'ordre superieur dans les categories semi-additives (1969) (1)
Collected papers of Kustaa Inkeri (1992) (1)
B.K. = Before Kummer (1979) (1)
The Naïve Approach (1979) (1)
Results on fixed points, combs and generalized formal power series (1992) (1)
One the existence of fields with few discrete valuations. (1964) (1)
A theorem on linear transformations of torsion-free modules of infinite rank (1963) (1)
Remarks on exponential congruences and powerful numbers (1988) (1)
Collected papers of Leo Moser (2005) (1)
Higher ramification groups for rank one valuations (1967) (1)
Prime Numbers, Friends Who Give Problems: A Trialogue With Papa Paulo (2016) (1)
A remark on Polignac’s conjecture (2009) (1)
The Work of Kummer on Fermat’s Last Theorem (1982) (1)
Solving parametrized systems of Pell equations (2005) (1)
Multiplicative Structures on Power Series and the Construction of Skewfields (1996) (1)
How Many Prime Numbers Are There (1996) (1)
On Orderable Fields (1969) (1)
Collected papers of Ruggiero Torelli (1995) (1)
Collected papers of Giacomo Albanese (1996) (1)
A short note on the equations of Fermat and Catalan (1992) (1)
An extension of Sophie Germain's method to a wide class of diophantine equations. (1985) (1)
Automorphisms of the ordered multiplicative group of positive rational numbers (1994) (1)
The differential spectrum of a ring (1973) (1)
Review: André Weil, Number theory, an approach through history from Hammurapi to Legendre (1985) (1)
Some Fundamental Methods in the Theory of Diophantine Equations (1986) (1)
A property of automorphisms of an infinite Galois extension (1966) (1)
Lecture—Recent Results on Fermat's Last Theorem (1977) (1)
Meta-noetherian rings (1976) (1)
After Kummer, a New Light (1979) (1)
On square factors of terms of binary recurring sequences and the $ABC$ Conjecture (2001) (1)
How Are the Prime Numbers Distributed (1996) (1)
Explicit Solutions of Certain Systems of Pell Equations (2012) (0)
The Decomposition of Prime Ideals in Galois Extensions (2001) (0)
AN EXISTENCE THEOREM FOR FIELDS (2016) (0)
Characters and Gaussian Sums (2001) (0)
Corrections to my paper „On ordered modules“ (1969) (0)
Galois Groups of Algebraic Extensions of Infinite Degree (1999) (0)
Zeta-Functions and L-Series (2001) (0)
Valuations of a Field (1999) (0)
Higher ramification groups for rank one valuations (1970) (0)
Decomposition and Inertia Theory (1999) (0)
Binary recurring sequences and powers. II. (1999) (0)
The Great Prime Mysteries (2017) (0)
Paulo Came with a Lasso (2017) (0)
Absolute Values of Fields (1999) (0)
Collected papers of Wayne L. McDaniel (2001) (0)
Money and Primes (2017) (0)
Collected papers of Satoshi Suzuki (1994) (0)
Trying Hard to Find Primes (2017) (0)
A Formula, A Formula, Please (2017) (0)
The Power of Class Field Theory (1979) (0)
On a question of Anne Marie Nicolas concerning valuation rings (1982) (0)
New Numbers and Functions (2017) (0)
Wolfgang Krull – Life, Work and Influence (1999) (0)
Unique Factorization Domains, Ideals, and Principal Ideal Domains (2001) (0)
Tell Me: Which is the Largest Prime? (2017) (0)
Collected papers of Mario Fiorentini (2000) (0)
Dedicated to my friend Marco Fontanu on his 50th birthday (2005) (0)
On the decomposition theory for Krull valuations (1962) (0)
Erratum to: The approximation to a fixed point (2013) (0)
Erratum to: The approximation to a fixed point (2013) (0)
Collected papers of Norman Alling (1998) (0)
Primes in Arithmetic Progressions (2001) (0)
How Natural Numbers are Made Out of Primes (2017) (0)
Fermat Numbers are Friendly. Are They Primes (2017) (0)
Generalized Ultrametric Spaces I (eng) (1996) (0)
Collected papers of Peter Roquette (2002) (0)
Valuation Characterizations of Dedekind Domains (1999) (0)
Fermat’s Last Theorem for Regular Prime Exponents (2001) (0)
SOME EXAMPLES OF VALUED FIELDSPAULO (1995) (0)
Estimates for the Discriminant (2001) (0)
Density zero results for elliptic curves without complex multiplication (1998) (0)
Primes After Dinner: Bad Dreams? (2017) (0)
Power Series and the Structure of Complete Valued Fields (1999) (0)
A note on Catalan's equation (1986) (0)
What are Prime Numbers (2017) (0)
The Early History of Fermat’s Last Theorem (1979) (0)
Miscellaneous Results About the Class Number of Quadratic Fields (2001) (0)
The Old Man Still Knows (2017) (0)
The Fundamental Theorem of Abelian Extensions (2001) (0)
Heuristic and Probabilistic Results about Prime Numbers (1996) (0)
The ascending chain condition for real ideas (1986) (0)
This World is Perfect (2017) (0)
I record dei numeri primi (1990) (0)
A Letter from Dieudonné (2015) (0)
Testing for Primality and Factorization (2017) (0)
Another Paulo! Is a Dialogue of Three Possible? (2017) (0)
A Glimpse of Krull Valuations (1999) (0)
Ideals, Valuations, and Divisors in Algebraic Extensions of Infinite Degree over ℚ (1999) (0)
Some examples of lattice-orders in real closed fields (1993) (0)
Extensions of Valuations: Numerical Relations (1999) (0)
Excerpt from "The Grothendieck I Knew: Telling, Not Hiding, Not Judging" (2019) (0)
Uniqueness of Extensions of Valuations and Poly-Complete Fields (1999) (0)
Longueurs de modules constructibles et valuations (1971) (0)
More on Cyclotomic Extensions (2001) (0)
Local Methods for Cyclotomic Fields (2001) (0)
Polynomials and Henselian Valued Fields (1999) (0)
The approximation to a fixed point (2013) (0)
Density results for families of diophantine equations (1993) (0)
On a question of Anne Marie Nicolas concerning chains of submodules (1983) (0)
Are There Functions Defining Prime Numbers (1996) (0)
Mysteries in Sequences: More But Not All (2017) (0)
Algebra group : September 1972 - August 1973 (1973) (0)
Extensions of Valuations (1999) (0)
The Decomposition of Ideals (2001) (0)
The End and the Beginning (2017) (0)
Paying My Debt (2017) (0)
Miscellaneous Results About the Class Number of Cyclotomic Fields (2001) (0)
Unfriendly Numbers from a Friend of Fermat’s (2017) (0)
The square-free kernel of x^2^n-a^2^n (2002) (0)
On the Riemann-Roch theorem (1961) (0)
The Norm and Classes of Ideals (2001) (0)
A Letter from Dieudonné (2015) (0)
Linear representations of groups (1967) (0)
The After “Math” of Gauss (2017) (0)
Complements and Miscellaneous Numerical Examples (2001) (0)
Finite sets of binary forms (2006) (0)
Can You Tell Me All About Congruences (2017) (0)
Which Special Kinds of Primes Have Been Considered (1996) (0)
Beautiful Old Elementary Arithmetic (2017) (0)
Infinite families of nonprincipal prime ideals (1992) (0)
Division is Harder than Multiplication (2017) (0)
The Relative Trace, Norm, Discriminant, and Different (2001) (0)
Some results on group rings(講演記録) (1970) (0)
Fermat's last theorem : récent developments. (1979) (0)
Integral Basis, Discriminant (2001) (0)
MULTIPLE PATTERNS OF k-TUPLES OF INTEGERS (2011) (0)
Collected papers of Karl Egil Aubert (1992) (0)
The Frobenius Automorphism and the Splitting of Prime Ideals (2001) (0)

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What Are Paulo Ribenboim's Academic Contributions?

Paulo Ribenboim is most known for their academic work in the field of mathematics. They are also known for their academic work in the fields of

Paulo Ribenboim has made the following academic contributions:

The Little Book of Bigger Primes

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