# find-zeros

`station__zeta__find-zeros` · external (needs EXECUTION_BACKEND_URL configured) · domain `zeta` · pv-relevance `non-pv`

Find zeros of ζ(s) on the critical line (σ=1/2) between t_low and t_high. Returns a list of zero locations with refined positions.

> **Note:** This tool routes through an external execution backend. If `EXECUTION_BACKEND_URL` is unset on the server, calls return JSON-RPC error `-32603 "Tool execution backend not configured"`. Tools with `backend: native` execute in-process and are always callable.

## Agent metadata

- `idempotent`: unknown
- `read_only`: unknown
- `expected_latency_ms`: unknown (not yet contract-tested)
- `cost_tokens_estimate`: unknown

## Input schema

- `t_low` *number* (required) — Lower bound of imaginary part to search
- `t_high` *number* (required) — Upper bound of imaginary part to search
- `step` *number* — Search step size (default 0.5)

## Example call

```json
POST /api/mcp
Content-Type: application/json

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/call",
  "params": {
    "name": "station__zeta__find-zeros",
    "arguments": {
      "t_low": 0,
      "t_high": 0
    }
  }
}
```

## Related

- [/tools](/tools) — all 3062 tools
- [/tools/zeta__find-zeros](/tools/zeta__find-zeros) — HTML page
- [/tools/zeta__find-zeros/json](/tools/zeta__find-zeros/json) — JSON form (agent-friendly)
- [/api/mcp](/api/mcp) — endpoint
- [/AGENTS.md](/AGENTS.md) — agent guide