diff --git a/evm/src/recursive_verifier.rs b/evm/src/recursive_verifier.rs
index 800ee461..000efce9 100644
--- a/evm/src/recursive_verifier.rs
+++ b/evm/src/recursive_verifier.rs
@@ -181,8 +181,8 @@ fn verify_stark_proof_with_challenges_circuit<
     let degree_bits = proof.recover_degree_bits(inner_config);
     let zeta_pow_deg = builder.exp_power_of_2_extension(challenges.stark_zeta, degree_bits);
     let z_h_zeta = builder.sub_extension(zeta_pow_deg, one);
-    let (l_1, l_last) =
-        eval_l_1_and_l_last_circuit(builder, degree_bits, challenges.stark_zeta, z_h_zeta);
+    let (l_0, l_last) =
+        eval_l_0_and_l_last_circuit(builder, degree_bits, challenges.stark_zeta, z_h_zeta);
     let last =
         builder.constant_extension(F::Extension::primitive_root_of_unity(degree_bits).inverse());
     let z_last = builder.sub_extension(challenges.stark_zeta, last);
@@ -191,7 +191,7 @@ fn verify_stark_proof_with_challenges_circuit<
         builder.zero_extension(),
         challenges.stark_alphas.clone(),
         z_last,
-        l_1,
+        l_0,
         l_last,
     );
 
@@ -254,7 +254,7 @@ fn verify_stark_proof_with_challenges_circuit<
     );
 }
 
-fn eval_l_1_and_l_last_circuit<F: RichField + Extendable<D>, const D: usize>(
+fn eval_l_0_and_l_last_circuit<F: RichField + Extendable<D>, const D: usize>(
     builder: &mut CircuitBuilder<F, D>,
     log_n: usize,
     x: ExtensionTarget<D>,
@@ -263,12 +263,12 @@ fn eval_l_1_and_l_last_circuit<F: RichField + Extendable<D>, const D: usize>(
     let n = builder.constant_extension(F::Extension::from_canonical_usize(1 << log_n));
     let g = builder.constant_extension(F::Extension::primitive_root_of_unity(log_n));
     let one = builder.one_extension();
-    let l_1_deno = builder.mul_sub_extension(n, x, n);
+    let l_0_deno = builder.mul_sub_extension(n, x, n);
     let l_last_deno = builder.mul_sub_extension(g, x, one);
     let l_last_deno = builder.mul_extension(n, l_last_deno);
 
     (
-        builder.div_extension(z_x, l_1_deno),
+        builder.div_extension(z_x, l_0_deno),
         builder.div_extension(z_x, l_last_deno),
     )
 }
diff --git a/evm/src/verifier.rs b/evm/src/verifier.rs
index 9b56422d..3f5a5a88 100644
--- a/evm/src/verifier.rs
+++ b/evm/src/verifier.rs
@@ -133,7 +133,7 @@ where
     };
 
     let degree_bits = proof.recover_degree_bits(config);
-    let (l_1, l_last) = eval_l_1_and_l_last(degree_bits, challenges.stark_zeta);
+    let (l_0, l_last) = eval_l_0_and_l_last(degree_bits, challenges.stark_zeta);
     let last = F::primitive_root_of_unity(degree_bits).inverse();
     let z_last = challenges.stark_zeta - last.into();
     let mut consumer = ConstraintConsumer::<F::Extension>::new(
@@ -143,7 +143,7 @@ where
             .map(|&alpha| F::Extension::from_basefield(alpha))
             .collect::<Vec<_>>(),
         z_last,
-        l_1,
+        l_0,
         l_last,
     );
     let num_permutation_zs = stark.num_permutation_batches(config);
@@ -204,10 +204,10 @@ where
     Ok(())
 }
 
-/// Evaluate the Lagrange polynomials `L_1` and `L_n` at a point `x`.
-/// `L_1(x) = (x^n - 1)/(n * (x - 1))`
-/// `L_n(x) = (x^n - 1)/(n * (g * x - 1))`, with `g` the first element of the subgroup.
-fn eval_l_1_and_l_last<F: Field>(log_n: usize, x: F) -> (F, F) {
+/// Evaluate the Lagrange polynomials `L_0` and `L_(n-1)` at a point `x`.
+/// `L_0(x) = (x^n - 1)/(n * (x - 1))`
+/// `L_(n-1)(x) = (x^n - 1)/(n * (g * x - 1))`, with `g` the first element of the subgroup.
+fn eval_l_0_and_l_last<F: Field>(log_n: usize, x: F) -> (F, F) {
     let n = F::from_canonical_usize(1 << log_n);
     let g = F::primitive_root_of_unity(log_n);
     let z_x = x.exp_power_of_2(log_n) - F::ONE;
@@ -222,10 +222,10 @@ mod tests {
     use plonky2::field::polynomial::PolynomialValues;
     use plonky2::field::types::Field;
 
-    use crate::verifier::eval_l_1_and_l_last;
+    use crate::verifier::eval_l_0_and_l_last;
 
     #[test]
-    fn test_eval_l_1_and_l_last() {
+    fn test_eval_l_0_and_l_last() {
         type F = GoldilocksField;
         let log_n = 5;
         let n = 1 << log_n;
@@ -234,7 +234,7 @@ mod tests {
         let expected_l_first_x = PolynomialValues::selector(n, 0).ifft().eval(x);
         let expected_l_last_x = PolynomialValues::selector(n, n - 1).ifft().eval(x);
 
-        let (l_first_x, l_last_x) = eval_l_1_and_l_last(log_n, x);
+        let (l_first_x, l_last_x) = eval_l_0_and_l_last(log_n, x);
         assert_eq!(l_first_x, expected_l_first_x);
         assert_eq!(l_last_x, expected_l_last_x);
     }
diff --git a/field/src/zero_poly_coset.rs b/field/src/zero_poly_coset.rs
index 18cc3238..8d63bc69 100644
--- a/field/src/zero_poly_coset.rs
+++ b/field/src/zero_poly_coset.rs
@@ -51,8 +51,8 @@ impl<F: Field> ZeroPolyOnCoset<F> {
         packed
     }
 
-    /// Returns `L_1(x) = Z_H(x)/(n * (x - 1))` with `x = w^i`.
-    pub fn eval_l1(&self, i: usize, x: F) -> F {
+    /// Returns `L_0(x) = Z_H(x)/(n * (x - 1))` with `x = w^i`.
+    pub fn eval_l_0(&self, i: usize, x: F) -> F {
         // Could also precompute the inverses using Montgomery.
         self.eval(i) * (self.n * (x - F::ONE)).inverse()
     }
diff --git a/plonky2/src/plonk/plonk_common.rs b/plonky2/src/plonk/plonk_common.rs
index 4f92d732..e947353b 100644
--- a/plonky2/src/plonk/plonk_common.rs
+++ b/plonky2/src/plonk/plonk_common.rs
@@ -64,31 +64,31 @@ pub(crate) fn eval_zero_poly<F: Field>(n: usize, x: F) -> F {
     x.exp_u64(n as u64) - F::ONE
 }
 
-/// Evaluate the Lagrange basis `L_1` with `L_1(1) = 1`, and `L_1(x) = 0` for other members of an
+/// Evaluate the Lagrange basis `L_0` with `L_0(1) = 1`, and `L_0(x) = 0` for other members of the
 /// order `n` multiplicative subgroup.
-pub(crate) fn eval_l_1<F: Field>(n: usize, x: F) -> F {
+pub(crate) fn eval_l_0<F: Field>(n: usize, x: F) -> F {
     if x.is_one() {
         // The code below would divide by zero, since we have (x - 1) in both the numerator and
         // denominator.
         return F::ONE;
     }
 
-    // L_1(x) = (x^n - 1) / (n * (x - 1))
+    // L_0(x) = (x^n - 1) / (n * (x - 1))
     //        = Z(x) / (n * (x - 1))
     eval_zero_poly(n, x) / (F::from_canonical_usize(n) * (x - F::ONE))
 }
 
-/// Evaluates the Lagrange basis L_1(x), which has L_1(1) = 1 and vanishes at all other points in
+/// Evaluates the Lagrange basis L_0(x), which has L_0(1) = 1 and vanishes at all other points in
 /// the order-`n` subgroup.
 ///
 /// Assumes `x != 1`; if `x` could be 1 then this is unsound.
-pub(crate) fn eval_l_1_circuit<F: RichField + Extendable<D>, const D: usize>(
+pub(crate) fn eval_l_0_circuit<F: RichField + Extendable<D>, const D: usize>(
     builder: &mut CircuitBuilder<F, D>,
     n: usize,
     x: ExtensionTarget<D>,
     x_pow_n: ExtensionTarget<D>,
 ) -> ExtensionTarget<D> {
-    // L_1(x) = (x^n - 1) / (n * (x - 1))
+    // L_0(x) = (x^n - 1) / (n * (x - 1))
     //        = Z(x) / (n * (x - 1))
     let one = builder.one_extension();
     let neg_one = builder.neg_one();
diff --git a/plonky2/src/plonk/vanishing_poly.rs b/plonky2/src/plonk/vanishing_poly.rs
index ab0ba53b..303f698b 100644
--- a/plonky2/src/plonk/vanishing_poly.rs
+++ b/plonky2/src/plonk/vanishing_poly.rs
@@ -10,7 +10,7 @@ use crate::plonk::circuit_builder::CircuitBuilder;
 use crate::plonk::circuit_data::CommonCircuitData;
 use crate::plonk::config::GenericConfig;
 use crate::plonk::plonk_common;
-use crate::plonk::plonk_common::eval_l_1_circuit;
+use crate::plonk::plonk_common::eval_l_0_circuit;
 use crate::plonk::vars::{EvaluationTargets, EvaluationVars, EvaluationVarsBaseBatch};
 use crate::util::partial_products::{check_partial_products, check_partial_products_circuit};
 use crate::util::reducing::ReducingFactorTarget;
@@ -41,17 +41,17 @@ pub(crate) fn eval_vanishing_poly<
 
     let constraint_terms = evaluate_gate_constraints(common_data, vars);
 
-    // The L_1(x) (Z(x) - 1) vanishing terms.
+    // The L_0(x) (Z(x) - 1) vanishing terms.
     let mut vanishing_z_1_terms = Vec::new();
     // The terms checking the partial products.
     let mut vanishing_partial_products_terms = Vec::new();
 
-    let l1_x = plonk_common::eval_l_1(common_data.degree(), x);
+    let l_0_x = plonk_common::eval_l_0(common_data.degree(), x);
 
     for i in 0..common_data.config.num_challenges {
         let z_x = local_zs[i];
         let z_gx = next_zs[i];
-        vanishing_z_1_terms.push(l1_x * (z_x - F::Extension::ONE));
+        vanishing_z_1_terms.push(l_0_x * (z_x - F::Extension::ONE));
 
         let numerator_values = (0..common_data.config.num_routed_wires)
             .map(|j| {
@@ -135,7 +135,7 @@ pub(crate) fn eval_vanishing_poly_base_batch<
     let mut numerator_values = Vec::with_capacity(num_routed_wires);
     let mut denominator_values = Vec::with_capacity(num_routed_wires);
 
-    // The L_1(x) (Z(x) - 1) vanishing terms.
+    // The L_0(x) (Z(x) - 1) vanishing terms.
     let mut vanishing_z_1_terms = Vec::with_capacity(num_challenges);
     // The terms checking the partial products.
     let mut vanishing_partial_products_terms = Vec::new();
@@ -152,11 +152,11 @@ pub(crate) fn eval_vanishing_poly_base_batch<
 
         let constraint_terms = PackedStridedView::new(&constraint_terms_batch, n, k);
 
-        let l1_x = z_h_on_coset.eval_l1(index, x);
+        let l_0_x = z_h_on_coset.eval_l_0(index, x);
         for i in 0..num_challenges {
             let z_x = local_zs[i];
             let z_gx = next_zs[i];
-            vanishing_z_1_terms.push(l1_x * z_x.sub_one());
+            vanishing_z_1_terms.push(l_0_x * z_x.sub_one());
 
             numerator_values.extend((0..num_routed_wires).map(|j| {
                 let wire_value = vars.local_wires[j];
@@ -332,12 +332,12 @@ pub(crate) fn eval_vanishing_poly_circuit<
         evaluate_gate_constraints_circuit(builder, common_data, vars,)
     );
 
-    // The L_1(x) (Z(x) - 1) vanishing terms.
+    // The L_0(x) (Z(x) - 1) vanishing terms.
     let mut vanishing_z_1_terms = Vec::new();
     // The terms checking the partial products.
     let mut vanishing_partial_products_terms = Vec::new();
 
-    let l1_x = eval_l_1_circuit(builder, common_data.degree(), x, x_pow_deg);
+    let l_0_x = eval_l_0_circuit(builder, common_data.degree(), x, x_pow_deg);
 
     // Holds `k[i] * x`.
     let mut s_ids = Vec::new();
@@ -350,8 +350,8 @@ pub(crate) fn eval_vanishing_poly_circuit<
         let z_x = local_zs[i];
         let z_gx = next_zs[i];
 
-        // L_1(x) Z(x) = 0.
-        vanishing_z_1_terms.push(builder.mul_sub_extension(l1_x, z_x, l1_x));
+        // L_0(x) (Z(x) - 1) = 0.
+        vanishing_z_1_terms.push(builder.mul_sub_extension(l_0_x, z_x, l_0_x));
 
         let mut numerator_values = Vec::new();
         let mut denominator_values = Vec::new();
diff --git a/starky/src/recursive_verifier.rs b/starky/src/recursive_verifier.rs
index 7f20d89b..04858d55 100644
--- a/starky/src/recursive_verifier.rs
+++ b/starky/src/recursive_verifier.rs
@@ -102,8 +102,8 @@ fn verify_stark_proof_with_challenges_circuit<
 
     let zeta_pow_deg = builder.exp_power_of_2_extension(challenges.stark_zeta, degree_bits);
     let z_h_zeta = builder.sub_extension(zeta_pow_deg, one);
-    let (l_1, l_last) =
-        eval_l_1_and_l_last_circuit(builder, degree_bits, challenges.stark_zeta, z_h_zeta);
+    let (l_0, l_last) =
+        eval_l_0_and_l_last_circuit(builder, degree_bits, challenges.stark_zeta, z_h_zeta);
     let last =
         builder.constant_extension(F::Extension::primitive_root_of_unity(degree_bits).inverse());
     let z_last = builder.sub_extension(challenges.stark_zeta, last);
@@ -112,7 +112,7 @@ fn verify_stark_proof_with_challenges_circuit<
         builder.zero_extension(),
         challenges.stark_alphas,
         z_last,
-        l_1,
+        l_0,
         l_last,
     );
 
@@ -170,7 +170,7 @@ fn verify_stark_proof_with_challenges_circuit<
     );
 }
 
-fn eval_l_1_and_l_last_circuit<F: RichField + Extendable<D>, const D: usize>(
+fn eval_l_0_and_l_last_circuit<F: RichField + Extendable<D>, const D: usize>(
     builder: &mut CircuitBuilder<F, D>,
     log_n: usize,
     x: ExtensionTarget<D>,
@@ -179,12 +179,12 @@ fn eval_l_1_and_l_last_circuit<F: RichField + Extendable<D>, const D: usize>(
     let n = builder.constant_extension(F::Extension::from_canonical_usize(1 << log_n));
     let g = builder.constant_extension(F::Extension::primitive_root_of_unity(log_n));
     let one = builder.one_extension();
-    let l_1_deno = builder.mul_sub_extension(n, x, n);
+    let l_0_deno = builder.mul_sub_extension(n, x, n);
     let l_last_deno = builder.mul_sub_extension(g, x, one);
     let l_last_deno = builder.mul_extension(n, l_last_deno);
 
     (
-        builder.div_extension(z_x, l_1_deno),
+        builder.div_extension(z_x, l_0_deno),
         builder.div_extension(z_x, l_last_deno),
     )
 }
diff --git a/starky/src/verifier.rs b/starky/src/verifier.rs
index 306d3d14..efb3d29c 100644
--- a/starky/src/verifier.rs
+++ b/starky/src/verifier.rs
@@ -78,7 +78,7 @@ where
             .unwrap(),
     };
 
-    let (l_1, l_last) = eval_l_1_and_l_last(degree_bits, challenges.stark_zeta);
+    let (l_0, l_last) = eval_l_0_and_l_last(degree_bits, challenges.stark_zeta);
     let last = F::primitive_root_of_unity(degree_bits).inverse();
     let z_last = challenges.stark_zeta - last.into();
     let mut consumer = ConstraintConsumer::<F::Extension>::new(
@@ -88,7 +88,7 @@ where
             .map(|&alpha| F::Extension::from_basefield(alpha))
             .collect::<Vec<_>>(),
         z_last,
-        l_1,
+        l_0,
         l_last,
     );
     let permutation_data = stark.uses_permutation_args().then(|| PermutationCheckVars {
@@ -144,10 +144,10 @@ where
     Ok(())
 }
 
-/// Evaluate the Lagrange polynomials `L_1` and `L_n` at a point `x`.
-/// `L_1(x) = (x^n - 1)/(n * (x - 1))`
-/// `L_n(x) = (x^n - 1)/(n * (g * x - 1))`, with `g` the first element of the subgroup.
-fn eval_l_1_and_l_last<F: Field>(log_n: usize, x: F) -> (F, F) {
+/// Evaluate the Lagrange polynomials `L_0` and `L_(n-1)` at a point `x`.
+/// `L_0(x) = (x^n - 1)/(n * (x - 1))`
+/// `L_(n-1)(x) = (x^n - 1)/(n * (g * x - 1))`, with `g` the first element of the subgroup.
+fn eval_l_0_and_l_last<F: Field>(log_n: usize, x: F) -> (F, F) {
     let n = F::from_canonical_usize(1 << log_n);
     let g = F::primitive_root_of_unity(log_n);
     let z_x = x.exp_power_of_2(log_n) - F::ONE;
@@ -189,10 +189,10 @@ mod tests {
     use plonky2::field::polynomial::PolynomialValues;
     use plonky2::field::types::Field;
 
-    use crate::verifier::eval_l_1_and_l_last;
+    use crate::verifier::eval_l_0_and_l_last;
 
     #[test]
-    fn test_eval_l_1_and_l_last() {
+    fn test_eval_l_0_and_l_last() {
         type F = GoldilocksField;
         let log_n = 5;
         let n = 1 << log_n;
@@ -201,7 +201,7 @@ mod tests {
         let expected_l_first_x = PolynomialValues::selector(n, 0).ifft().eval(x);
         let expected_l_last_x = PolynomialValues::selector(n, n - 1).ifft().eval(x);
 
-        let (l_first_x, l_last_x) = eval_l_1_and_l_last(log_n, x);
+        let (l_first_x, l_last_x) = eval_l_0_and_l_last(log_n, x);
         assert_eq!(l_first_x, expected_l_first_x);
         assert_eq!(l_last_x, expected_l_last_x);
     }