Let $k$ an even positive integer and $p$ an odd prime number such that $p-1|k$. Let $D>0$ be ranging over fundamental discriminants of real quadratic fields. Consider the following modular form $$G_{k,D}=\frac{1}{2}L(1-k,(\frac{D}{.}))+\sum_{n\geq1}(\sum_{d|n}(\frac{D}{d})d^{k-1})q^n.$$
- Is there any result about $\mod{p}$ congruences for the function $\sigma_{k-1,D}(n)=\sum_{d|n}(\frac{D}{d})d^{k-1}$ ?
- How can we use the above modular form to deduce $\mod{p}$ congruence for $\frac{1}{2}L(1-k,(\frac{D}{.}))$ ?
$\begingroup$
$\endgroup$
2
-
$\begingroup$ This seems to be a virtually exact duplicate of of mathoverflow.net/questions/263248/… $\endgroup$– David LoefflerMar 2, 2017 at 7:46
-
5$\begingroup$ Possible duplicate of Special values of Dirichlet L-functions at negative integers $\endgroup$– David LoefflerMar 2, 2017 at 7:47
Add a comment
|