sagemathgh-39387: minor changes about faster binomial in modular
    
just using the faster binomial method

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: sagemath#39387
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert

Author: Release Manager

src/sage/modular/dirichlet.py

@@ -62,7 +62,7 @@
 import sage.rings.abc
 
 from sage.arith.functions import lcm
-from sage.arith.misc import bernoulli, binomial, factorial, kronecker, factor, gcd, fundamental_discriminant, euler_phi, valuation
+from sage.arith.misc import bernoulli, factorial, kronecker, factor, gcd, fundamental_discriminant, euler_phi, valuation
 from sage.categories.map import Map
 from sage.categories.objects import Objects
 from sage.categories.rings import Rings
@@ -724,7 +724,7 @@ def bernoulli(self, k, algorithm='recurrence', cache=True, **opts):
             def S(n):
                 return sum(v[r] * r**n for r in range(1, N))
 
-            ber = sum(binomial(k, j) * bernoulli(j, **opts) *
+            ber = sum(ZZ(k).binomial(j) * bernoulli(j, **opts) *
                       N**(j - 1) * S(k - j) for j in range(k + 1))
         elif algorithm == "definition":
             # This is better since it computes the same thing, but requires

src/sage/modular/pollack_stevens/dist.pyx

@@ -27,7 +27,7 @@ REFERENCES:
 # ****************************************************************************
 import operator
 
-from sage.arith.misc import binomial, bernoulli
+from sage.arith.misc import bernoulli
 from sage.categories.fields import Fields
 from sage.matrix.constructor import matrix
 from sage.matrix.matrix cimport Matrix
@@ -1129,7 +1129,7 @@ cdef class Dist_vector(Dist):
         """
         # assert self._moments[0][0]==0, "not total measure zero"
         # print("result accurate modulo p^",self.moment(0).valuation(self.p) )
-        # v=[0 for j in range(0,i)]+[binomial(j,i)*bernoulli(j-i) for j in range(i,M)]
+        # v=[0 for j in range(i)]+[binomial(j,i)*bernoulli(j-i) for j in range(i,M)]
         M = self.precision_relative()
         R = self.parent().base_ring()
         K = R.fraction_field()
@@ -1142,7 +1142,7 @@ cdef class Dist_vector(Dist):
             # bernoulli(1) = -1/2; the only nonzero odd Bernoulli number
             v[m] += m * minhalf * scalar
             for j in range(m - 1, M, 2):
-                v[j] += binomial(j, m - 1) * bern[(j - m + 1) // 2] * scalar
+                v[j] += ZZ(j).binomial(m - 1) * bern[(j - m + 1) // 2] * scalar
         p = self.parent().prime()
         cdef Dist_vector ans
         if p == 0:

src/sage/modular/pollack_stevens/padic_lseries.py

@@ -121,7 +121,7 @@ def __init__(self, symb, gamma=None, quadratic_twist=1, precision=None):
         self._gamma = gamma
         self._quadratic_twist = quadratic_twist
         self._precision = precision
-        self._cinf = ZZ(1)  # is set when called for an elliptic curve
+        self._cinf = ZZ.one()  # is set when called for an elliptic curve
 
     def __getitem__(self, n):
         r"""
@@ -373,7 +373,7 @@ def _basic_integral(self, a, j):
         ap = ap * kronecker(D, p)
         K = pAdicField(p, M)
         symb_twisted = symb.evaluate_twisted(a, D)
-        return sum(binomial(j, r) *
+        return sum(ZZ(j).binomial(r) *
                    ((a - ZZ(K.teichmuller(a))) ** (j - r)) *
                    (p ** r) *
                    symb_twisted.moment(r) for r in range(j + 1)) / ap