Ralph S. Phillips

7.9k total citations · 1 hit paper
91 papers, 4.2k citations indexed

About

Ralph S. Phillips is a scholar working on Mathematical Physics, Applied Mathematics and Computational Theory and Mathematics. According to data from OpenAlex, Ralph S. Phillips has authored 91 papers receiving a total of 4.2k indexed citations (citations by other indexed papers that have themselves been cited), including 55 papers in Mathematical Physics, 27 papers in Applied Mathematics and 26 papers in Computational Theory and Mathematics. Recurrent topics in Ralph S. Phillips's work include Spectral Theory in Mathematical Physics (16 papers), Advanced Algebra and Geometry (16 papers) and Advanced Mathematical Modeling in Engineering (15 papers). Ralph S. Phillips is often cited by papers focused on Spectral Theory in Mathematical Physics (16 papers), Advanced Algebra and Geometry (16 papers) and Advanced Mathematical Modeling in Engineering (15 papers). Ralph S. Phillips collaborates with scholars based in United States, Israel and Denmark. Ralph S. Phillips's co-authors include Peter D. Lax, Peter Sarnak, Alexander Lubotzky, G. Lumer, Brad Osgood, Cathleen S. Morawetz, Hubert M. James, J. F. Adams, Rafe Mazzeo and Zeév Rudnick and has published in prestigious journals such as Proceedings of the National Academy of Sciences, Annals of Mathematics and Communications on Pure and Applied Mathematics.

In The Last Decade

Ralph S. Phillips

88 papers receiving 3.3k citations

Hit Papers

Ramanujan graphs 1988 2026 2000 2013 1988 100 200 300 400 500
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.

  1. Ramanujan graphs
    1988 566 citations Ralph S. Phillips, Peter Sarnak et al. profile →

Peers — A (Enhanced Table)

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

Name h Career Trend Papers Cites
Ralph S. Phillips United States 32 2.1k 1.5k 1.2k 932 470 91 4.2k
W. J. Thron United States 22 1.1k 0.5× 1.6k 1.1× 1.5k 1.2× 1.1k 1.1× 894 1.9× 87 4.7k
Yitzhak Katznelson United States 21 1.5k 0.7× 1.1k 0.8× 650 0.5× 796 0.9× 336 0.7× 63 3.1k
V. S. Varadarajan United States 23 1.8k 0.8× 734 0.5× 690 0.6× 1.2k 1.3× 807 1.7× 81 3.5k
M. Г. Крейн Germany 23 2.6k 1.2× 2.6k 1.8× 2.2k 1.8× 460 0.5× 408 0.9× 53 5.7k
Einar Hille United States 17 1.2k 0.6× 1.6k 1.1× 801 0.7× 751 0.8× 219 0.5× 55 3.6k
Lars V. Ahlfors United States 24 1.6k 0.7× 2.8k 1.9× 750 0.6× 2.9k 3.1× 293 0.6× 49 5.2k
Richard S. Palais United States 28 2.0k 0.9× 2.0k 1.4× 851 0.7× 1.9k 2.1× 555 1.2× 64 4.4k
T. J. Rivlin United States 23 606 0.3× 1.7k 1.2× 1.4k 1.2× 523 0.6× 297 0.6× 71 5.3k
F. E. J. Linton United States 13 2.6k 1.2× 1.2k 0.8× 750 0.6× 2.0k 2.1× 1.3k 2.8× 20 4.5k
Karl Stromberg United States 15 926 0.4× 1.0k 0.7× 683 0.6× 522 0.6× 269 0.6× 29 2.7k

Countries citing papers authored by Ralph S. Phillips

Since Specialization
Citations

This map shows the geographic impact of Ralph S. Phillips'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 Ralph S. Phillips with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Ralph S. Phillips more than expected).

Fields of papers citing papers by Ralph S. Phillips

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Ralph S. Phillips. 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 Ralph S. Phillips. The network helps show where Ralph S. Phillips may publish in the future.

Co-authorship network of co-authors of Ralph S. Phillips

This figure shows the co-authorship network connecting the top 25 collaborators of Ralph S. Phillips. A scholar is included among the top collaborators of Ralph S. Phillips 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 Ralph S. Phillips. Ralph S. Phillips is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Phillips, Ralph S. & Zeév Rudnick. (1994). The Circle Problem in the Hyperbolic Plane. Journal of Functional Analysis. 121(1). 78–116. 25 indexed citations
2.
Phillips, Ralph S. & Peter Sarnak. (1992). Perturbation theory for the Laplacian on automorphic functions. Journal of the American Mathematical Society. 5(1). 1–32. 27 indexed citations
3.
Osgood, Brad, Ralph S. Phillips, & Peter Sarnak. (1988). Extremals of determinants of Laplacians. Journal of Functional Analysis. 80(1). 148–211. 274 indexed citations
4.
Osgood, Brad, Ralph S. Phillips, & Peter Sarnak. (1988). Compact isospectral sets of surfaces. Journal of Functional Analysis. 80(1). 212–234. 101 indexed citations
5.
Phillips, Ralph S., et al.. (1987). Scattering theory for the wave equation on a hyperbolic manifold. Journal of Functional Analysis. 74(2). 346–398. 4 indexed citations
6.
Lax, Peter D. & Ralph S. Phillips. (1982). The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces. Journal of Functional Analysis. 46(3). 280–350. 121 indexed citations
7.
Lax, Peter D. & Ralph S. Phillips. (1980). Scattering theory for automorphic functions. Bulletin of the American Mathematical Society. 2(2). 261–295. 165 indexed citations
8.
Lax, Peter D. & Ralph S. Phillips. (1974). A scattering theory for automorphic functions. Project Euclid (Cornell University). 1–7. 9 indexed citations
9.
Lax, Peter D. & Ralph S. Phillips. (1972). Scattering Theory for the Acoustic Equation in an Even Number of Space Dimensions. Indiana University Mathematics Journal. 22(2). 101–134. 49 indexed citations
10.
Lax, Peter D. & Ralph S. Phillips. (1972). . Indiana University Mathematics Journal. 22(2). 101–101. 11 indexed citations
11.
Crandall, Michael G. & Ralph S. Phillips. (1968). On the extension problem for dissipative operators. Journal of Functional Analysis. 2(2). 147–176. 16 indexed citations
12.
Lax, Peter D., et al.. (1966). Correction to "On Matrices Whose Real Linear Combinations are Nonsingular". Proceedings of the American Mathematical Society. 17(4). 945–945. 3 indexed citations
13.
Adams, J. F., Peter D. Lax, & Ralph S. Phillips. (1965). On matrices whose real linear combinations are non-singular. Proceedings of the American Mathematical Society. 16(2). 318–322. 68 indexed citations
14.
Phillips, Ralph S.. (1957). Dissipative hyperbolic systems. Transactions of the American Mathematical Society. 86(1). 109–173. 42 indexed citations
15.
Phillips, Ralph S.. (1957). Dissipative Hyperbolic Systems. Transactions of the American Mathematical Society. 86(1). 109–109. 8 indexed citations
16.
Phillips, Ralph S.. (1953). Perturbation Theory for Semi-Groups of Linear Operators. Transactions of the American Mathematical Society. 74(2). 199–199. 42 indexed citations
17.
Phillips, Ralph S.. (1951). A note on ergodic theory. Proceedings of the American Mathematical Society. 2(4). 663–670. 4 indexed citations
18.
Phillips, Ralph S.. (1951). Spectral theory for semi-groups of linear operators. Transactions of the American Mathematical Society. 71(3). 393–415. 18 indexed citations
19.
Phillips, Ralph S.. (1951). Spectral Theory for Semi-Groups of Linear Operators. Transactions of the American Mathematical Society. 71(3). 393–393. 13 indexed citations
20.
Phillips, Ralph S.. (1951). On one-parameter semi-groups of linear transformations. Proceedings of the American Mathematical Society. 2(2). 234–237. 15 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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