added riemann zeta function algorithm

math/riemann_zeta_function.c

@@ -0,0 +1,46 @@
+/**
+ * @file
+ * @brief Algorithm to calculate the Riemann Zeta function for a given real number.
+ * @details https://en.wikipedia.org/wiki/Riemann_zeta_function
+ * @author ["Nunito (https://github.com/nunniii) <mateusnss@protonmail.ch>"]
+ */
+
+#include <math.h>
+#include <complex.h>
+#include <stdio.h>
+
+/**
+ * @brief Calculate the Riemann Zeta function for a given real number s.
+ * @param real_part - Real part of the complex number s
+ * @param num_terms - Number of terms in the series to sum
+ * @return The value of the Riemann Zeta function at s
+ * @warning This implementation is a simple approximation,
+ * see the purpose of the num_terms_to_sum variable in the scope of main().
+ *
+ * @b Algorithm Complexity:
+ *      - Time: O(num_terms)
+ *      - Space: O(1)
+ */
+double complex riemann_zeta(double real_part, int num_terms)
+{
+    double complex result = 0.0 + 0.0 * I; // as a complex number
+
+    for (int n = 1; n <= num_terms; ++n)
+    {
+        result += 1.0 / (cpow(n, real_part));
+    }
+    return result;
+}
+
+int main() {
+    // Example of use:
+    double real_part = 7.0;  // Real of s
+    int num_terms_to_sum = 100;  // Number of terms that will be added to the series, (the greater  the quantity, the greater the precision)
+
+    // zeta_value(double real_part, int num_terms) return double
+    double complex zeta_value = riemann_zeta(real_part, num_terms_to_sum);
+
+    printf("Zeta(%lf) = %.10lf + %.10lfi\n", real_part, creal(zeta_value), cimag(zeta_value));
+
+    return 0;
+}