Hugh L. Montgomery

5.5k total citations · 3 hit papers
66 papers, 2.4k citations indexed

About

Hugh L. Montgomery is a scholar working on Algebra and Number Theory, Geometry and Topology and Mathematical Physics. According to data from OpenAlex, Hugh L. Montgomery has authored 66 papers receiving a total of 2.4k indexed citations (citations by other indexed papers that have themselves been cited), including 39 papers in Algebra and Number Theory, 17 papers in Geometry and Topology and 16 papers in Mathematical Physics. Recurrent topics in Hugh L. Montgomery's work include Analytic Number Theory Research (37 papers), Advanced Mathematical Identities (14 papers) and Meromorphic and Entire Functions (9 papers). Hugh L. Montgomery is often cited by papers focused on Analytic Number Theory Research (37 papers), Advanced Mathematical Identities (14 papers) and Meromorphic and Entire Functions (9 papers). Hugh L. Montgomery collaborates with scholars based in United States, United Kingdom and Germany. Hugh L. Montgomery's co-authors include R. C. Vaughan, Robert C. Vaughan, Andrew Odlyzko, Jeffrey C. Lagarias, Norman Levinson, Per Enflo, Bernard Beauzamy, Enrico Bombieri, Jeffrey D. Vaaler and S. M. Gonek and has published in prestigious journals such as Mathematics of Computation, Annals of Mathematics and Lecture notes in mathematics.

In The Last Decade

Hugh L. Montgomery

57 papers receiving 2.1k citations

Hit Papers

Topics in Multiplicative Number Theory 1971 2026 1989 2007 1971 1994 2006 100 200 300
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. Topics in Multiplicative Number Theory
    1971 368 citations Hugh L. Montgomery Lecture notes in mathematics profile →
  2. Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis
    1994 320 citations Hugh L. Montgomery profile →
  3. Multiplicative Number Theory I: Classical Theory
    2006 310 citations Hugh L. Montgomery, R. C. Vaughan CERN Document Server (European Organization for Nuclear Research) profile →

Peers — A (Enhanced Table)

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

Name h Career Trend Papers Cites
Hugh L. Montgomery United States 21 1.8k 870 769 710 549 66 2.4k
Kenneth S. Williams Canada 24 1.4k 0.7× 861 1.0× 512 0.7× 533 0.8× 380 0.7× 304 2.3k
M. N. Huxley United Kingdom 16 947 0.5× 484 0.6× 416 0.5× 299 0.4× 283 0.5× 71 1.3k
Emmanuel Kowalski Switzerland 20 1.7k 0.9× 939 1.1× 1.2k 1.5× 700 1.0× 177 0.3× 73 2.1k
Andrew Granville Canada 20 1.0k 0.6× 624 0.7× 338 0.4× 577 0.8× 127 0.2× 124 1.5k
Lowell Schoenfeld United States 13 976 0.5× 544 0.6× 262 0.3× 407 0.6× 197 0.4× 22 1.5k
Morris Newman United States 22 702 0.4× 568 0.7× 361 0.5× 525 0.7× 262 0.5× 169 1.9k
A. Baker United Kingdom 23 842 0.5× 1.0k 1.2× 731 1.0× 181 0.3× 283 0.5× 42 2.0k
Henryk Iwaniec United States 36 4.6k 2.5× 2.3k 2.7× 2.9k 3.8× 1.7k 2.4× 529 1.0× 123 5.5k
L. N. Vaserstein United States 21 807 0.4× 768 0.9× 804 1.0× 644 0.9× 125 0.2× 77 1.5k
Sergeĭ Konyagin Russia 18 544 0.3× 325 0.4× 291 0.4× 500 0.7× 343 0.6× 139 1.4k

Countries citing papers authored by Hugh L. Montgomery

Since Specialization
Citations

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

Fields of papers citing papers by Hugh L. Montgomery

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Hugh L. Montgomery. 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 Hugh L. Montgomery. The network helps show where Hugh L. Montgomery may publish in the future.

Co-authorship network of co-authors of Hugh L. Montgomery

This figure shows the co-authorship network connecting the top 25 collaborators of Hugh L. Montgomery. A scholar is included among the top collaborators of Hugh L. Montgomery 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 Hugh L. Montgomery. Hugh L. Montgomery 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.
Goldston, D. A., et al.. (2023). Small gaps and small spacings between zeta zeros. Acta Arithmetica. 210. 2 indexed citations
2.
Montgomery, Hugh L., Ashkan Nikeghbali, & Michael Th. Rassias. (2017). Exploring the Riemann Zeta Function. CERN Document Server (European Organization for Nuclear Research). 9 indexed citations
3.
Gonek, S. M. & Hugh L. Montgomery. (2012). Zeros of a Family of Approximations of the Riemann Zeta-Function. International Mathematics Research Notices. 2013(20). 4712–4733. 6 indexed citations
4.
Gallagher, P. X. & Hugh L. Montgomery. (2010). A note on Burgess’s estimate. Mathematical Notes. 88(3-4). 321–329. 6 indexed citations
5.
Maier, Helmut & Hugh L. Montgomery. (2009). The sum of the Möbius function. Bulletin of the London Mathematical Society. 41(2). 213–226. 7 indexed citations
6.
Brüdern, Jörg, Hugh L. Montgomery, & R. C. Vaughan. (2008). Analytic Number Theory. Oberwolfach Reports. 5(1). 669–746. 25 indexed citations
7.
Montgomery, Hugh L. & R. C. Vaughan. (2006). Multiplicative Number Theory I: Classical Theory. CERN Document Server (European Organization for Nuclear Research). 310 indexed citations breakdown →
8.
Montgomery, Hugh L.. (1994). Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis. 320 indexed citations breakdown →
9.
Montgomery, Hugh L.. (1988). Minimal theta functions. Glasgow Mathematical Journal. 30(1). 75–85. 53 indexed citations
10.
Montgomery, Hugh L. & Andrew Odlyzko. (1988). Large deviations of sums of independent random variables. Acta Arithmetica. 49(4). 427–434. 12 indexed citations
11.
Montgomery, Hugh L. & R. C. Vaughan. (1986). On the Distribution of Reduced Residues. Annals of Mathematics. 123(2). 311–311. 15 indexed citations
12.
Montgomery, Hugh L.. (1980). An exponential polynomial formed with the Legendre symbol. Acta Arithmetica. 37. 375–380. 17 indexed citations
13.
Montgomery, Hugh L., et al.. (1979). Elementary Problems: E2744,E2779-E2784. American Mathematical Monthly. 86(6). 503–503. 1 indexed citations
14.
Montgomery, Hugh L. & R. C. Vaughan. (1977). Exponential sums with multiplicative coefficients. Inventiones mathematicae. 43(1). 69–82. 78 indexed citations
15.
Montgomery, Hugh L.. (1976). Polynomials in many variables. French digital mathematics library (Numdam). 17(1). 1–6. 2 indexed citations
16.
Levinson, Norman & Hugh L. Montgomery. (1974). Zeros of the derivatives of the Riemann zeta-function. Acta Mathematica. 133(0). 49–65. 52 indexed citations
17.
Montgomery, Hugh L. & R. C. Vaughan. (1973). ERROR TERMS IN ADDITIVE PRIME NUMBER THEORY. The Quarterly Journal of Mathematics. 24(1). 207–216. 15 indexed citations
18.
Montgomery, Hugh L. & R. C. Vaughan. (1973). The large sieve. Mathematika. 20(2). 119–134. 178 indexed citations
19.
Montgomery, Hugh L.. (1971). Topics in Multiplicative Number Theory. Lecture notes in mathematics. 368 indexed citations breakdown →
20.
Montgomery, Hugh L.. (1965). Distribution of irregular primes. Illinois Journal of Mathematics. 9(4). 9 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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