This L-function has central value . Seriously?

What are the analytic implications for very small?

This, .

The major problem of studying and higher K-theory for algebraic varieties is that we do not know whether the K-groups are finitely generated, even for curves!

Chao Li presented various theorems and conjectures in the blogpost K2 and L-functions of elliptic curves, for example:

On the Hasse-Weil L-functions of singular K3 surfaces over

A singular K3 surface is a K3 surface with Picard rank 20. The word “singular” does not mean it has singularities; instead, it means that the moduli space of these surfaces is isolated (but still dense in the whole K3 moduli), so the surfaces are “singled” out.

What about a branch of math called small number analysis?

The phrase “small number analysis” is originated from a Zhihu answer as 小数解析, where the answerer states that a new branch of math called “small number analysis” will arise if there would be a refutation of the Riemann hypothesis; this branch of math is just analytic number theory in the range where the Riemann hypothesis is still true.

The real quadratic number fields with discriminants 229, 257, 733, 761, 1129 and 1229 have their orders of the class groups divisible by 3, so there are cubic fields with such discriminants (Hint: the Hilbert class field of a galois field is galois).

And there are totally imaginary fields with such discriminants, except 733. Why is 733 an exception?

Klein’s high-dimensional continued fractions and regulators

All number fields mentioned in this post should be understood as totally real number fields.

1. What are Klein’s high-dimensional continued fractions?

Collection of conductors of real cyclotomic fields that has class number > 1, i.e. the main table of Rene Schoof

163 191 229 257 277 313 349 397 401 457 491 521 547 577 607 631 641 709 733 761 821 827 829 853 857 877 937 941 953 977 1009 1063 1069 1093 1129 1153 1229 1231 1297 1373 1381 1399 1429 1459 1489 1567 1601 1697 1699 1777 1789 1831 1861 1873 1879 1889 1901 1951 1987 2029 2081 2089 2113 2131 2153 2161 2213 2311 2351 2381 2417 2437 2473 2557 2617 2621 2659 2677 2689 2713 2753 2777 2797 2803 2857 2917 2927 3001 3037 3041 3121 3137 3181 3217 3221 3229 3253 3271 3301 3313 3433 3469 3517 3529 3547 3571 3581 3697 3727 3877 3889 3931 4001 4049 4073 4099 4177 4201 4219 4229 4241 4261 4297 4327 4339 4357 4409 4441 4457 4481 4493 4561 4567 4591 4597 4603 4639 4649 4657 4729 4783 4789 4793 4801 4817 4861 4889 4933 4937 4993 5051 5081 5101 5119 5197 5209 5261 5273 5281 5297 5333 5413 5417 5437 5441 5477 5479 5501 5521 5531 5557 5581 5641 5659 5701 5741 5779 5821 5827 5953 6037 6053 6073 6079 6113 6133 6163 6229 6247 6257 6301 6337 6361 6421 6449 6481 6521 6529 6553 6577 6581 6637 6673 6709 6737 6781 6833 6949 6961 6991 6997 7027 7057 7229 7297 7333 7351 7369 7411 7417 7481 7489 7529 7537 7561 7573 7589 7621 7639 7673 7687 7753 7817 7841 7867 7873 7879 7937 8011 8017 8069 8101 8161 8191 8209 8269 8287 8297 8317 8377 8389 8431 8501 8563 8581 8597 8629 8647 8681 8689 8713 8731 8761 8831 8837 8887 8893 9001 9013 9029 9041 9049 9109 9127 9133 9161 9181 9241 9277 9281 9283 9293 9319 9337 9377 9391 9413 9421 9511 9521 9551 9601 9613 9649 9689 9697 9721 9749 9817 9829 9833 9857 9907

It’s still unknown whether there are infinitely many number fields of class number 1.

So I decided to investigate more number fields uncovered in the Wikipedia article.