mathematics

Hans Peter Schlickewei

Hans Peter Schlickewei is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hans Peter Schlickewei rather than just read about it. In short: Hans Peter Schlickewei (born 1947) is a German mathematician, specializing in number theory and, in particular, the theory of transcendental numbers. Schlickewei received his doctorate in 1975 at the University of Freiburg under the supervision of Theodor Schneider.

Key takeaways

Hans Peter Schlickewei belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hans Peter Schlickewei to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hans Peter Schlickewei from memory before moving on to harder problems.

Reference excerpt

Hans Peter Schlickewei (born 1947) is a German mathematician, specializing in number theory and, in particular, the theory of transcendental numbers. Schlickewei received his doctorate in 1975 at the University of Freiburg under the supervision of Theodor Schneider. Schlickewei is a professor at the University of Marburg. He proved in 1976 the p-adic generalization of the subspace theorem of Wolfgang M. Schmidt. Schlickewei's theorem implies the Thue-Siegel-Roth theorem, whose p-adic analogue was already proved in 1958 by David Ridout. In 1998, Schlickewei was an invited speaker with talk The Subspace Theorem and Applications at the International Congress of Mathematicians in Berlin.

Selected publications Schlickewei, H. P. (1976). "Die p-adische Verallgemeinerung des Satzes von Thue-Siegel-Roth-Schmidt". J. Reine Angew. Math. 1976 (288): 86–105. doi:10.1515/crll.1976.288.86. S2CID 115523021. Schinzel, A.; Schlickewei, H.; Schmidt, W. (1980). "Small solutions of quadratic congruences and small fractional parts of quadratic forms". Acta Arithmetica. 37 (1): 241–248. doi:10.4064/aa-37-1-241-248. Schlickewei, H. P. (1990). "S-unit equations over number fields". Invent. Math. 102: 95–107. Bibcode:1990InMat.102...95S. doi:10.1007/BF01233421. S2CID 120614908. Van Der Poorten, A. J.; Schlickewei, H. P. (1991). "Additive relations in fields". Journal of the Australian Mathematical Society, Series A. 51: 154–170. doi:10.1017/S144678870003336X. Schlickewei, H. P. (1993). "Multiplicities of algebraic linear recurrrences". Acta Mathematica. 170 (2): 151–180. doi:10.1007/BF02392784. Schlickewei, H. P. (1996). "Multiplicities of recurrence sequences". Acta Mathematica. 176 (2): 171–243. doi:10.1007/BF02551582. Schlickewei, H. P. (1997). "The multiplicity of binary recurrences". Invent. Math. 129 (11): 11–36. Bibcode:1997InMat.129...11S. doi:10.1007/s002220050156. S2CID 121677668. Schlickewei, H. P.; Schmidt, W. P. (2000). "The number of solutions of polynomial-exponential equations". Compositio Math. 120 (2): 193–225. doi:10.1023/A:1001719425893. S2CID 123405472. Evertse, J.-H.; Schlickewei, H. P.; Schmidt, W. M. (2002). "Linear Equations in Variables which Lie in a Multiplicative Group". The Annals of Mathematics. 155 (3): 807. arXiv:math/0409604. doi:10.2307/3062133. JSTOR 3062133. S2CID 5727031. Approximation of algebraic numbers, pp. 107–170 in: D. Masser, Yu. V. Nesterenko, W. Schmidt, M. Waldschmidt (eds.): Diophantine Approximation, Lectures CIME Summer School 2000, Springer 2003

References

External links "003 On Polynomial Exponential Equations by H. P. Schlickewei, Philipps-University Marburg". YouTube. matsciencechannel. 26 December 2013.

Illustrations

Worked examples

Example 1 — a first encounter with Hans Peter Schlickewei

Start with the simplest possible case. Write down what Hans Peter Schlickewei claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hans Peter Schlickewei before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hans Peter Schlickewei ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hans Peter Schlickewei

In research: Hans Peter Schlickewei appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hans Peter Schlickewei in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hans Peter Schlickewei is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1947 births, 20th-century German mathematicians, 21st-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Hans Peter Schlickewei outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Hans Peter Schlickewei” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Hans Peter Schlickewei in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hans Peter Schlickewei means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hans Peter Schlickewei out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hans Peter Schlickewei in simple terms?

Why does Hans Peter Schlickewei matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hans Peter Schlickewei?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hans Peter Schlickewei.