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Added a link to Mark Grant's comment as per suggestion of @LSpice
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Daniele Tampieri
Daniele Tampieri
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I agree with Mark Grant's commentMark Grant's comment above, since I also remember that the first proofs of the Prime number theorem given by J. Hadamard and C. J. de la Vallée Poussin, were quite long and involved: however, many mathematicians worked to simplify their proofs. Currently, you can find reasonably short proofs in (graduate) textbooks as [1], chapter 6, pp. 200-238: you may read that chapter and figure out if your students will be able to attend fruitfully a lecture dealing with an abridged version of it. On my side, I remark that there are many interesting tools developed/introduced for the proof, for example the Tauberian theory wich is an interesting topic per se.

[1] Veech, W. A. (1967), A second course in complex analysis, New York-Amsterdam: W.A. Benjamin, Inc., pp. IX+246, MR0220903, Zbl 0145.29901.

I agree with Mark Grant's comment above, since I also remember that the first proofs of the Prime number theorem given by J. Hadamard and C. J. de la Vallée Poussin, were quite long and involved: however, many mathematicians worked to simplify their proofs. Currently, you can find reasonably short proofs in (graduate) textbooks as [1], chapter 6, pp. 200-238: you may read that chapter and figure out if your students will be able to attend fruitfully a lecture dealing with an abridged version of it. On my side, I remark that there are many interesting tools developed/introduced for the proof, for example the Tauberian theory wich is an interesting topic per se.

[1] Veech, W. A. (1967), A second course in complex analysis, New York-Amsterdam: W.A. Benjamin, Inc., pp. IX+246, MR0220903, Zbl 0145.29901.

I agree with Mark Grant's comment above, since I also remember that the first proofs of the Prime number theorem given by J. Hadamard and C. J. de la Vallée Poussin, were quite long and involved: however, many mathematicians worked to simplify their proofs. Currently, you can find reasonably short proofs in (graduate) textbooks as [1], chapter 6, pp. 200-238: you may read that chapter and figure out if your students will be able to attend fruitfully a lecture dealing with an abridged version of it. On my side, I remark that there are many interesting tools developed/introduced for the proof, for example the Tauberian theory wich is an interesting topic per se.

[1] Veech, W. A. (1967), A second course in complex analysis, New York-Amsterdam: W.A. Benjamin, Inc., pp. IX+246, MR0220903, Zbl 0145.29901.

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Daniele Tampieri
Daniele Tampieri
  • 6.4k
  • 7
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  • 45

I agree with Mark GrantGrant's comment above, since I also remember that the first proofs of the Prime number theorem given by J. Hadamard and C. J. de la Vallée Poussin, were quite long and involved: however, many mathematicians worked to simplify their proofs. Currently, you can find reasonably short proofs it in (graduate) textbooks as the one of Veech (1967) (ch.[1], chapter 6, pp. 200-238): you canmay read that chapter and figure out if your students will be able to attend fruitfully a lecture dealing with an abridged version of it. On my side, I remark that there are many interesting tools developed/introduced for the proof, for example the Tauberian theory wich is an interesting topic per se.

[1] Veech, W. A. (1967), A second course in complex analysis, New York-Amsterdam: W.A. Benjamin, Inc., pp. IX+246, MR0220903MR0220903, Zbl 0145Zbl 0145.29901.29901

I agree with Mark Grant, since I also remember that the first proofs of the Prime number theorem given by J. Hadamard and C. J. de la Vallée Poussin, were quite long and involved: however, many mathematicians worked to simplify their proofs. Currently you can find proofs it in (graduate) textbooks as the one of Veech (1967) (ch. 6, pp. 200-238): you can read that chapter and figure out if your students will be able to attend fruitfully a lecture dealing with an abridged version of it. On my side, I remark that there are many interesting tools developed/introduced for the proof, for example the Tauberian theory wich is an interesting topic per se.

[1] Veech, W. A. (1967), A second course in complex analysis, New York-Amsterdam: W.A. Benjamin, Inc., pp. IX+246, MR0220903, Zbl 0145.29901

I agree with Mark Grant's comment above, since I also remember that the first proofs of the Prime number theorem given by J. Hadamard and C. J. de la Vallée Poussin, were quite long and involved: however, many mathematicians worked to simplify their proofs. Currently, you can find reasonably short proofs in (graduate) textbooks as [1], chapter 6, pp. 200-238: you may read that chapter and figure out if your students will be able to attend fruitfully a lecture dealing with an abridged version of it. On my side, I remark that there are many interesting tools developed/introduced for the proof, for example the Tauberian theory wich is an interesting topic per se.

[1] Veech, W. A. (1967), A second course in complex analysis, New York-Amsterdam: W.A. Benjamin, Inc., pp. IX+246, MR0220903, Zbl 0145.29901.

typo
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Daniele Tampieri
Daniele Tampieri
  • 6.4k
  • 7
  • 30
  • 45

I agree with Mark Grant, since I also remember that the first proofs of the Prime number theorem given by J. Hadamard and C. J. de la Vallée Poussin, were quite long and involved: however, many mathematicians worked to simplify their proofs. Currently you can find proofs it in (graduate) textbooks as the one of Veech (1967) (ch. 6, pp. 200-238): you can read that chapter and figure out if your studentstudents will be able to attend fruitfully a lecture dealing with an abridged version of it. On my side, I remark that there are many interesting tools developed/introduced for the proof, for example the Tauberian theory wich is an interesting topic per se.

[1] Veech, W. A. (1967), A second course in complex analysis, New York-Amsterdam: W.A. Benjamin, Inc., pp. IX+246, MR0220903, Zbl 0145.29901

I agree with Mark Grant, since I also remember that the first proofs of the Prime number theorem given by J. Hadamard and C. J. de la Vallée Poussin, were quite long and involved: however, many mathematicians worked to simplify their proofs. Currently you can find proofs it in (graduate) textbooks as the one of Veech (1967) (ch. 6, pp. 200-238): you can read that chapter and figure out if your student will be able to attend fruitfully a lecture dealing with an abridged version of it. On my side, I remark that there are many interesting tools developed/introduced for the proof, for example the Tauberian theory wich is an interesting topic per se.

[1] Veech, W. A. (1967), A second course in complex analysis, New York-Amsterdam: W.A. Benjamin, Inc., pp. IX+246, MR0220903, Zbl 0145.29901

I agree with Mark Grant, since I also remember that the first proofs of the Prime number theorem given by J. Hadamard and C. J. de la Vallée Poussin, were quite long and involved: however, many mathematicians worked to simplify their proofs. Currently you can find proofs it in (graduate) textbooks as the one of Veech (1967) (ch. 6, pp. 200-238): you can read that chapter and figure out if your students will be able to attend fruitfully a lecture dealing with an abridged version of it. On my side, I remark that there are many interesting tools developed/introduced for the proof, for example the Tauberian theory wich is an interesting topic per se.

[1] Veech, W. A. (1967), A second course in complex analysis, New York-Amsterdam: W.A. Benjamin, Inc., pp. IX+246, MR0220903, Zbl 0145.29901

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Daniele Tampieri
Daniele Tampieri
  • 6.4k
  • 7
  • 30
  • 45