Helmut Maier

<h2 id="education">Education</h2>
<p>Helmut Maier graduated with a Diploma in Mathematics from the <a href="/facts/University_of_Ulm/dNv34Jxv">University of Ulm</a> in 1976, under the supervision of Hans-Egon Richert. He received his PhD from the <a href="/facts/University_of_Minnesota/vN1uQvP5">University of Minnesota</a> in 1981, under the supervision of J. Ian Richards.
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<h2 id="research-and-academic-positions">Research and academic positions</h2>
<p>Maier's PhD thesis was an extension of his paper <i>Chains of large gaps between consecutive primes</i>.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> In this paper Maier applied for the first time what is now known as <a href="/facts/Maier%2527s_matrix_method/LobSPIme">Maier's matrix method</a>. This method later on led him and other mathematicians to the discovery of unexpected irregularities in the distribution of prime numbers.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a> There have been various other applications of Maier's Matrix Method, such as on irreducible polynomials and on strings of consecutive primes in the same residue class.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a>
</p><p>After postdoctoral positions at the <a href="/facts/University_of_Michigan/6e1Ea5xh">University of Michigan</a> and the <a href="/facts/Institute_for_Advanced_Study%2c_Princeton/jQQCURKt">Institute for Advanced Study, Princeton</a>, Maier obtained a permanent position at the <a href="/facts/University_of_Georgia/SkqyQmok">University of Georgia</a>. While in Georgia he proved that the usual formulation of the Cramér model for the distribution of prime numbers is wrong. This was a completely unexpected result.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> Jointly with <a href="/facts/Carl_Pomerance/mmKNsTUr">Carl Pomerance</a> he studied the values of Euler's φ(<i>n</i>)-function
and large gaps between primes.  During the same period Maier investigated as well 
the size of the coefficients of cyclotomic polynomials and later collaborated with <a href="/facts/Sergei_Konyagin/WqHJkj4e">Sergei Konyagin</a>
and <a href="/facts/Eduard_Wirsing/7r3M4r62">Eduard Wirsing</a> on this topic. He also collaborated with <a href="/facts/Hugh_Lowell_Montgomery/k1VI3W69">Hugh Lowell Montgomery</a> on the size of the sum of the 
<a href="/facts/M%25C3%25B6bius_function/geuvVfqS">Möbius function</a> under the assumption of the <a href="/facts/Riemann_Hypothesis/Td8Jq5r0">Riemann Hypothesis</a>. Maier and <a href="/facts/G%25C3%25A9rald_Tenenbaum/pytj23Hm">Gérald Tenenbaum</a>
in joint work investigated the sequence of divisors of integers, solving the famous <i>propinquity</i> problem of
<a href="/facts/Paul_Erd%25C5%2591s/63LoUTe1">Paul Erdős</a>.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> Since 1993, Maier has been a professor at the <a href="/facts/University_of_Ulm/dNv34Jxv">University of Ulm</a>, Germany.
</p><p>Collaborators of Helmut Maier
include <a href="/facts/Paul_Erd%25C5%2591s/63LoUTe1">Paul Erdős</a>, C. Feiler, <a href="/facts/John_Friedlander/aVTXUsVK">John Friedlander</a>, <a href="/facts/Andrew_Granville/EhFz6kyI">Andrew Granville</a>, D. Haase, A. J. Hildebrand, 
Michel Laurent Lapidus [fr], J. W. Neuberger, A. Sankaranarayanan, A. Sárközy, <a href="/facts/Wolfgang_P._Schleich/uAPQ1J9l">Wolfgang P. Schleich</a>, <a href="/facts/Cameron_Leigh_Stewart/5eEsc5Ce">Cameron Leigh Stewart</a>.
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<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Maier%2527s_matrix_method/LobSPIme">Maier's matrix method</a></li>
<li><a href="/facts/Maier%2527s_theorem/j4ff9yop">Maier's theorem</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="https://www.uni-ulm.de/mawi/zawa/personen/maier.html">Maier's webpage</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Lagarias, Jeffrey (2013). "Euler's constant: Euler's work and modern developments". Bulletin of the American Mathematical Society. 50 (4): 572. arXiv:1303.1856. doi:10.1090/s0273-0979-2013-01423-x. S2CID 119612431. <a href="/wiki/Jeffrey_Lagarias" target="_blank">/wiki/Jeffrey_Lagarias</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Granville, Andrew (1994). "Unexpected irregularities in the distribution of prime numbers". Proc. Intern. Congress Math., Zürich: 388–399. <a href="/wiki/Andrew_Granville" target="_blank">/wiki/Andrew_Granville</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Maier, Helmut (1981). "Chains of large gaps between consecutive primes". Advances in Mathematics. 39 (3): 257–269. doi:10.1016/0001-8708(81)90003-7. <a href="https://doi.org/10.1016%2F0001-8708%2881%2990003-7" target="_blank">https://doi.org/10.1016%2F0001-8708%2881%2990003-7</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Granville, Andrew (1994). "Unexpected irregularities in the distribution of prime numbers". Proc. Intern. Congress Math., Zürich: 388–399. <a href="/wiki/Andrew_Granville" target="_blank">/wiki/Andrew_Granville</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Monks, K.; Peluse, S.; Ye, L. (2013). "Strings of special primes in arithmetic progressions, (English summary)". Arch. Math. 101 (3): 219–234. arXiv:1407.1290. doi:10.1007/s00013-013-0544-x. S2CID 49020700. <a href="/wiki/Sarah_Peluse" target="_blank">/wiki/Sarah_Peluse</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>Shiu, D. K. L. (2000). "Strings of congruent primes". J. London Math. Soc. 61 (2): 359–373. doi:10.1112/s0024610799007863. S2CID 122851878. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>Granville, Andrew (1994). "Unexpected irregularities in the distribution of prime numbers". Proc. Intern. Congress Math., Zürich: 388–399. <a href="/wiki/Andrew_Granville" target="_blank">/wiki/Andrew_Granville</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
<li id="fn:8"><p>Maier, H.; Tenenbaum, G. (1984). "On the set of divisors of an integer" (PDF). Invent. Math. 76: 121–128. Bibcode:1984InMat..76..121M. doi:10.1007/bf01388495. hdl:2027.42/46612. S2CID 27684856. <a href="https://deepblue.lib.umich.edu/bitstream/2027.42/46612/1/222_2005_Article_BF01388495.pdf" target="_blank">https://deepblue.lib.umich.edu/bitstream/2027.42/46612/1/222_2005_Article_BF01388495.pdf</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li>
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Helmut Maier open-in-new

Helmut Maier