Daniel Shanks

3.5k total citations · 1 hit paper
102 papers, 2.0k citations indexed

About

Daniel Shanks is a scholar working on Algebra and Number Theory, Geometry and Topology and Theoretical Computer Science. According to data from OpenAlex, Daniel Shanks has authored 102 papers receiving a total of 2.0k indexed citations (citations by other indexed papers that have themselves been cited), including 52 papers in Algebra and Number Theory, 45 papers in Geometry and Topology and 21 papers in Theoretical Computer Science. Recurrent topics in Daniel Shanks's work include Analytic Number Theory Research (42 papers), Advanced Mathematical Identities (23 papers) and History and Theory of Mathematics (21 papers). Daniel Shanks is often cited by papers focused on Analytic Number Theory Research (42 papers), Advanced Mathematical Identities (23 papers) and History and Theory of Mathematics (21 papers). Daniel Shanks collaborates with scholars based in United States, Canada and Germany. Daniel Shanks's co-authors include Richard Bellman, P. Weinberger, W. J. LeVeque, Hywel C Williams, William W. Adams, Emma Lehmer, D. H. Lehmer, Henry B. Mann, J. W. Wrench and Mohan Lal and has published in prestigious journals such as Mathematics of Computation, American Journal of Physics and SIAM Review.

In The Last Decade

Daniel Shanks

89 papers receiving 1.4k citations

Hit Papers

align trajectories

What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

Non‐linear Transformations of Divergent and Slowly Convergent Sequences

1955 811 citations Daniel Shanks profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name	h						Papers	Cites
Daniel Shanks United States	19	671	585	303	281	249	102	2.0k
Andrzej Schinzel Poland	21	755 1.1×	970 1.7×	452 1.5×	433 1.5×	398 1.6×	170	2.3k
P. Túrán Hungary	21	573 0.9×	427 0.7×	543 1.8×	470 1.7×	218 0.9×	77	2.7k
Harley Flanders United States	18	196 0.3×	285 0.5×	368 1.2×	207 0.7×	76 0.3×	98	1.7k
Tom H. Koornwinder Netherlands	27	834 1.2×	768 1.3×	318 1.0×	844 3.0×	82 0.3×	99	2.7k
Henry C. Thacher United States	14	123 0.2×	203 0.3×	597 2.0×	234 0.8×	125 0.5×	57	2.2k
T. S. Chihara United States	19	558 0.8×	280 0.5×	767 2.5×	477 1.7×	122 0.5×	43	3.0k
Hassler Whitney United States	13	194 0.3×	785 1.3×	375 1.2×	603 2.1×	39 0.2×	18	2.0k
Charles F. Dunkl United States	23	549 0.8×	729 1.2×	308 1.0×	1.5k 5.4×	133 0.5×	113	3.4k
S. Sternberg United States	14	588 0.9×	1.6k 2.8×	213 0.7×	1.5k 5.3×	40 0.2×	25	3.1k
Yudell L. Luke United States	16	239 0.4×	120 0.2×	282 0.9×	192 0.7×	93 0.4×	91	2.4k

Countries citing papers authored by Daniel Shanks

Since Specialization

Citations

This map shows the geographic impact of Daniel Shanks's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Daniel Shanks with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Daniel Shanks more than expected).

Fields of papers citing papers by Daniel Shanks

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Daniel Shanks. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Daniel Shanks. The network helps show where Daniel Shanks may publish in the future.

Co-authorship network of co-authors of Daniel Shanks

This figure shows the co-authorship network connecting the top 25 collaborators of Daniel Shanks. A scholar is included among the top collaborators of Daniel Shanks based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Daniel Shanks. Daniel Shanks is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

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20 of 20 papers shown

1.

Shanks, Daniel. (1978). Corrigenda: “Gauss’s ternary form reduction and the 2-Sylow subgroup” (Math. Comp. 25 (1971), 837–853). Mathematics of Computation. 32(144). 1328–1329. 1 indexed citations

2.

Shanks, Daniel. (1976). Class groups of the quadratic fields found by F. Diaz y Diaz. Mathematics of Computation. 30(133). 173–178. 8 indexed citations

3.

Shanks, Daniel. (1976). Class Groups of the Quadratic Fields Found by F. Diaz y Diaz. Mathematics of Computation. 30(133). 173–173. 3 indexed citations

4.

Shanks, Daniel. (1974). The Simplest Cubic Fields. Mathematics of Computation. 28(128). 1137–1137. 29 indexed citations

5.

Shanks, Daniel, et al.. (1974). Brun's Constant. Mathematics of Computation. 28(125). 293–293. 1 indexed citations

6.

Shanks, Daniel & Mohan Lal. (1972). Bateman's Constants Reconsidered and the Distribution of Cubic Residues. Mathematics of Computation. 26(117). 265–265. 6 indexed citations

7.

Shanks, Daniel. (1972). New types of quadratic fields having three invariants divisible by 3. Journal of Number Theory. 4(6). 537–556. 21 indexed citations

8.

Shanks, Daniel. (1969). Corrigenda: “Solutions of the Diophantine equations 𝑥²+𝑦²=𝑙², 𝑦²+𝑧²=𝑚², 𝑧²+𝑥²=𝑛²” (Math. Comp. 20 (1966), 144–147) by M. Lal and W. J. Blundon. Mathematics of Computation. 23(105). 219–219. 1 indexed citations

9.

Shanks, Daniel. (1967). Generalized Euler and class numbers. Mathematics of Computation. 21(100). 689–694. 10 indexed citations

10.

Shanks, Daniel, et al.. (1967). On the Distribution of Mersenne Divisors. Mathematics of Computation. 21(97). 97–97. 3 indexed citations

11.

Shanks, Daniel, et al.. (1966). Questions concerning Khintchine’s constant and the efficient computation of regular continued fractions. Mathematics of Computation. 20(95). 444–448. 5 indexed citations

12.

Shanks, Daniel. (1964). Polylogarithms, Dirichlet Series, and Certain Constants. Mathematics of Computation. 18(86). 322–322. 3 indexed citations

13.

Shanks, Daniel. (1964). On maximal gaps between successive primes. Mathematics of Computation. 18(88). 646–651. 27 indexed citations

14.

Shanks, Daniel. (1964). On Maximal Gaps between Successive Primes. Mathematics of Computation. 18(88). 646–646. 26 indexed citations

15.

Shanks, Daniel, et al.. (1963). The Calculation of Certain Dirichlet Series. Mathematics of Computation. 17(82). 136–136. 11 indexed citations

16.

Shanks, Daniel, et al.. (1963). The calculation of certain Dirichlet series. Mathematics of Computation. 17(82). 136–154. 15 indexed citations

17.

Shanks, Daniel. (1959). Quadratic residues and the distribution of primes. Mathematics of Computation. 13(68). 272–284. 28 indexed citations

18.

Shanks, Daniel. (1956). A Study of Postulates: The “Thermodynamic” Derivation of the Adiabatic Gas Law. American Journal of Physics. 24(5). 352–354. 1 indexed citations

19.

Shanks, Daniel. (1954). A logarithm algorithm. Mathematics of Computation. 8(46). 60–64. 6 indexed citations

20.

Shanks, Daniel. (1951). A short proof of an identity of Euler. Proceedings of the American Mathematical Society. 2(5). 747–749. 30 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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