Daniel Shanks
American mathematician
Daniel Shanks's AcademicInfluence.com Rankings
Download Badge
Mathematics
Daniel Shanks's Degrees
- PhD Mathematics University of California, Berkeley
- Masters Mathematics University of California, Berkeley
- Bachelors Mathematics University of California, Berkeley
Similar Degrees You Can Earn
Why Is Daniel Shanks Influential?
(Suggest an Edit or Addition)According to Wikipedia, Daniel Charles Shanks was an American mathematician who worked primarily in numerical analysis and number theory. He was the first person to compute π to 100,000 decimal places. Life and education Shanks was born on January 17, 1917, in Chicago, Illinois. He is not related to the English mathematician William Shanks, who was also known for his computation of π. He earned his Bachelor of Science degree in physics from the University of Chicago in 1937, and a Ph.D. in Mathematics from the University of Maryland in 1954. Prior to obtaining his PhD, Shanks worked at the Aberdeen Proving Ground and the Naval Ordnance Laboratory, first as a physicist and then as a mathematician. During this period he wrote his PhD thesis, which completed in 1949, despite having never taken any graduate math courses.
Daniel Shanks's Published Works
Published Works
- Non‐linear Transformations of Divergent and Slowly Convergent Sequences (1955) (963)
- Class number, a theory of factorization, and genera (1971) (470)
- Solved and Unsolved Problems in Number Theory (1964) (243)
- On the Distribution of Parity in the Partition Function (1967) (73)
- The simplest cubic fields (1974) (72)
- On maximal gaps between successive primes (1964) (65)
- Strong primality tests that are not sufficient (1982) (63)
- Calculation of π to 100,000 Decimals (1962) (54)
- Quadratic Residues and the Distribution of Primes (1959) (49)
- A Necessary and Sufficient Condition for Primality, and Its Source (1972) (46)
- On Gauss’s class number problems (1969) (40)
- On the conjecture of Hardy & Littlewood concerning the number of primes of the form ²+ (1960) (40)
- The Second-Order Term in the Asymptotic Expansion of B(x) (1964) (40)
- Integer sequences having prescribed quadratic character (1970) (37)
- A SHORT PROOF OF AN IDENTITY OF EULER (1951) (34)
- A quadratic field of prime discriminant requiring three generators for its class group, and related theory (1972) (34)
- Gauss’s ternary form reduction and the 2-Sylow subgroup (1971) (26)
- Variations on a theorem of Landau. I (1966) (24)
- New types of quadratic fields having three invariants divisible by 3 (1972) (23)
- Calculation and applications of Epstein zeta functions (1975) (23)
- Simple groups of square order and interesting sequence of primes (1980) (21)
- The calculation of certain Dirichlet series (1963) (20)
- Brun's Constant (1974) (19)
- A sieve method for factoring numbers of the form ²+1 (1959) (17)
- A note on class-number one in pure cubic fields (1979) (15)
- Two theorems of Gauss (1958) (15)
- On the 3-rank of quadratic fields and the Euler product (1974) (15)
- Quadratic Fields with Four Invariants Divisible by 3 (1973) (14)
- THE NUMERICAL SOLUTION OF THE HEAT CONDUCTION EQUATION OCCURRING IN THE THEORY OF THERMAL EXPLOSIONS (1956) (14)
- Dihedral quartic approximations and series for π (1982) (14)
- Khintchine's Constant (1959) (13)
- Monochromatic Approximation of Blackbody Radiation (1956) (13)
- Variations on a Theorem of Landau. Part I (1966) (11)
- On numbers of the form $n^{4}+1$ (1961) (11)
- Fast primality tests for numbers less than 50 · 10 9 (1986) (10)
- Gunderson’s function in Fermat’s last theorem (1981) (10)
- Generalized Euler and class numbers (1967) (10)
- Supplementary data and remarks concerning a Hardy-Littlewood conjecture (1963) (9)
- Advanced Problems: 6403-6408 (1982) (9)
- On a Sequence Arising in Series for π (1984) (8)
- On a Sequence Arising in Series for π (1984) (8)
- A logarithm algorithm (1954) (8)
- Quadratic fields with 3-rank equal to 4 (1979) (8)
- Class groups of the quadratic fields found by F. Diaz y Diaz (1976) (8)
- A Note on Gaussian Twin Primes (1960) (8)
- Questions concerning Khintchine’s constant and the efficient computation of regular continued fractions (1966) (7)
- Bateman's Constants Reconsidered and the Distribution of Cubic Residues (1972) (7)
- 48 more solutions of Martin Davis's quaternary quartic equation (1995) (7)
- On the distribution of Mersenne divisors (1967) (7)
- Corrigendum: “Class groups of the quadratic fields found by F. Diaz y Diaz” (Math. Comp. 30 (1976), no. 133, 173–178) (1976) (6)
- Zeros of 2-adic L-functions and congruences for class numbers and fundamental units (1999) (5)
- Corrigenda: “Gauss’s ternary form reduction and the 2-Sylow subgroup” (Math. Comp. 25 (1971), 837–853) (1978) (5)
- Corrigendum: “Calculation and applications of Epstein zeta functions” (Math. Comp. 29 (1975), 271–287) (1975) (5)
- A NEW GENERAL FORMULA FOR REPRESENTING THE DRAG ON A MISSILE OVER THE ENTIRE RANGE OF MACH NUMBER (1957) (4)
- Lal's Constant and Generalizations (1967) (4)
- Polylogarithms, Dirichlet series, and certain constants (1964) (4)
- An Analogy Between Transients and Mathematical Sequences and Some Nonlinear Sequence-to-Sequence Transforms Suggested by It. Part 1 (1949) (4)
- Table errata: “Regular continued fractions for and ”, (Math. Comp. 25 (1971), 403); “Rational approximations to ” (ibid. 25 (1971), 387–392) by K. Y. Choong, D. E. Daykin and C. R. Rathbone (1976) (2)
- Integer Sequences Having Prescribed (1970) (2)
- A Study of Postulates: The “Thermodynamic” Derivation of the Adiabatic Gas Law (1956) (2)
- An Infinite Permutation (M. S. Klamkin) (1965) (2)
- On a sequence arising in series for pi (with an appendix by D. Zagier). (1984) (2)
- Corrigenda: “Quadratic fields with four invariants divisible by 3” (Math. Comp. 27 (1973), 183–187) by Daniel Shanks and Richard Serafin (1973) (2)
- An analytic criterion for the existence of infinitely many primes of the form $\frac{1}{2}(n^{2}+1)$ (1964) (2)
- On analogous theorems of Fredholm and Frame and on the inverse of a matrix (1955) (1)
- A Duality Relation in Exterior Ballistics (1964) (1)
- Corrigenda to: “Generalized Euler and class numbers “ (1968) (1)
- Corrigendum to: “On generating infinitely many solutions of the Diophantine equation ⁶+⁶+⁶=⁶+⁶+⁶” (Math. Comp. 24 (1970), 453–454) by Simcha Brudno (1971) (1)
- Corrigenda: “Solutions of the Diophantine equations ²+²=², ²+²=², ²+²=²” (Math. Comp. 20 (1966), 144–147) by M. Lal and W. J. Blundon (1969) (1)
- Corrigenda to: “The calculation of certain Dirichlet series” (1968) (1)
- Sums of Reciprocals to 1,000,000 (1975) (0)
- Table of the Greatest Prime Factor of N 2 + 1 for N = 1(1)185000 (1975) (0)
- Table errata: “A note on the Catalan-Dickson conjecture” (Math. Comp. 27 (1973), 189–192) (1973) (0)
- Advanced Problems: 6192-6197 (1978) (0)
- Advanced Problems: 6012-6017 (1975) (0)
- SQUFOF (an unfinished manuscript) (0)
- Advanced Problems: 6174-6179 (1977) (0)
- Corrigendum to: “Statistical study of digits of some square roots of integers in various bases” (Math. Comp. 24 (1970), 455–473) by W. A. Beyer, N. Metropolis and J. R. Neergaard (1971) (0)
- CALIBRATION OF THE HOPKINS BLASTMETER (1940) (0)
- Three Tables Concerning the Parity of the Partition Numbers p(n) for n < 2040000 (1976) (0)
This paper list is powered by the following services:
Other Resources About Daniel Shanks
What Schools Are Affiliated With Daniel Shanks?
Daniel Shanks is affiliated with the following schools: