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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="AlffSerreBound"></a>
AlffSerreBound
</h2>

Computes the Serre bound of a global function field.

<p><p>

<h3>
Syntax:
</h3>
<pre>b := AlffSerreBound(F);
b := AlffSerreBound(q, g);</pre>

<p>

<table>
<tr>
<td>global function field</td>
<td><pre>  F  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  q, g  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  b  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#AlffIharaBound">AlffIharaBound</a>, <a href="kashref.html#AlffPlacesDegOneNumBound">AlffPlacesDegOneNumBound</a>

<p>

<h3>
Description:
</h3>
Let g be the genus of a function field F over the exact
constant field {\Bbb F}_q. This function computes the
Serre bound (improvement of the Hasse-Weil bound) for the
number of places of degree one of F using the function
field or for given q and g.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>

<pre>

kash> AlffInit(FF(2,3));
"Defining global variables: k, w, kT, kTf, kTy, T, y, AlffGlobals"
kash> AlffOrders(y^3+T^3*y+T);
"Defining global variables: F, o, oi, one"
kash> AlffGenus(F);
3
kash> AlffSerreBound(F);
24
kash> AlffSerreBound(5, 7);
> 34

</pre>

<p>


<hr>

<p>
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